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Sample records for quantum monte carlo

  1. Quantum speedup of Monte Carlo methods

    PubMed Central

    Montanaro, Ashley

    2015-01-01

    Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

  2. Interaction picture density matrix quantum Monte Carlo

    SciTech Connect

    Malone, Fionn D. Lee, D. K. K.; Foulkes, W. M. C.; Blunt, N. S.; Shepherd, James J.; Spencer, J. S.

    2015-07-28

    The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

  3. Fast quantum Monte Carlo on a GPU

    NASA Astrophysics Data System (ADS)

    Lutsyshyn, Y.

    2015-02-01

    We present a scheme for the parallelization of quantum Monte Carlo method on graphical processing units, focusing on variational Monte Carlo simulation of bosonic systems. We use asynchronous execution schemes with shared memory persistence, and obtain an excellent utilization of the accelerator. The CUDA code is provided along with a package that simulates liquid helium-4. The program was benchmarked on several models of Nvidia GPU, including Fermi GTX560 and M2090, and the Kepler architecture K20 GPU. Special optimization was developed for the Kepler cards, including placement of data structures in the register space of the Kepler GPUs. Kepler-specific optimization is discussed.

  4. Quantum Monte Carlo calculations of light nuclei

    SciTech Connect

    Pieper, S.C.

    1998-12-01

    Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to eight nucleons. We have computed the ground and a few excited states of all such nuclei with Greens function Monte Carlo (GFMC) and all of the experimentally known excited states using variational Monte Carlo (VMC). The GFMC calculations show that for a given Hamiltonian, the VMC calculations of excitation spectra are reliable, but the VMC ground-state energies are significantly above the exact values. We find that the Hamiltonian we are using (which was developed based on {sup 3}H,{sup 4}He, and nuclear matter calculations) underpredicts the binding energy of p-shell nuclei. However our results for excitation spectra are very good and one can see both shell-model and collective spectra resulting from fundamental many-nucleon calculations. Possible improvements in the three-nucleon potential are also be discussed. {copyright} {ital 1998 American Institute of Physics.}

  5. Quantum Monte Carlo calculations of light nuclei

    SciTech Connect

    Pieper, Steven C.

    1998-12-21

    Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to eight nucleons. We have computed the ground and a few excited states of all such nuclei with Greens function Monte Carlo (GFMC) and all of the experimentally known excited states using variational Monte Carlo (VMC). The GFMC calculations show that for a given Hamiltonian, the VMC calculations of excitation spectra are reliable, but the VMC ground-state energies are significantly above the exact values. We find that the Hamiltonian we are using (which was developed based on {sup 3}H,{sup 4}He, and nuclear matter calculations) underpredicts the binding energy of p-shell nuclei. However our results for excitation spectra are very good and one can see both shell-model and collective spectra resulting from fundamental many-nucleon calculations. Possible improvements in the three-nucleon potential are also be discussed.

  6. Quantum Monte Carlo calculations of light nuclei.

    SciTech Connect

    Pieper, S. C.

    1998-08-25

    Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to eight nucleons. We have computed the ground and a few excited states of all such nuclei with Greens function Monte Carlo (GFMC) and all of the experimentally known excited states using variational Monte Carlo (VMC). The GFMC calculations show that for a given Hamiltonian, the VMC calculations of excitation spectra are reliable, but the VMC ground-state energies are significantly above the exact values. We find that the Hamiltonian we are using (which was developed based on {sup 3}H, {sup 4}He, and nuclear matter calculations) underpredicts the binding energy of p-shell nuclei. However our results for excitation spectra are very good and one can see both shell-model and collective spectra resulting from fundamental many-nucleon calculations. Possible improvements in the three-nucleon potential are also be discussed.

  7. Approaching chemical accuracy with quantum Monte Carlo.

    PubMed

    Petruzielo, F R; Toulouse, Julien; Umrigar, C J

    2012-03-28

    A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space. PMID:22462844

  8. Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization

    NASA Astrophysics Data System (ADS)

    Brady, Lucas T.; van Dam, Wim

    2016-03-01

    We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate quantum adiabatic optimization algorithms during a quantum tunneling process. Specifically we look at symmetric cost functions defined over n bits with a single potential barrier that a successful quantum adiabatic optimization algorithm will have to tunnel through. The height and width of this barrier depend on n , and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time. In this article we compare the strength of quantum adiabatic tunneling with that of path-integral quantum Monte Carlo methods. We find numerical evidence that quantum Monte Carlo algorithms will succeed in the same regimes where quantum adiabatic optimization succeeds.

  9. Interaction picture density matrix quantum Monte Carlo.

    PubMed

    Malone, Fionn D; Blunt, N S; Shepherd, James J; Lee, D K K; Spencer, J S; Foulkes, W M C

    2015-07-28

    The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible. PMID:26233116

  10. Linear-scaling quantum Monte Carlo calculations.

    PubMed

    Williamson, A J; Hood, R Q; Grossman, J C

    2001-12-10

    A method is presented for using truncated, maximally localized Wannier functions to introduce sparsity into the Slater determinant part of the trial wave function in quantum Monte Carlo calculations. When combined with an efficient numerical evaluation of these localized orbitals, the dominant cost in the calculation, namely, the evaluation of the Slater determinant, scales linearly with system size. This technique is applied to accurate total energy calculation of hydrogenated silicon clusters and carbon fullerenes containing 20-1000 valence electrons. PMID:11736525

  11. Applications of Maxent to quantum Monte Carlo

    SciTech Connect

    Silver, R.N.; Sivia, D.S.; Gubernatis, J.E. ); Jarrell, M. . Dept. of Physics)

    1990-01-01

    We consider the application of maximum entropy methods to the analysis of data produced by computer simulations. The focus is the calculation of the dynamical properties of quantum many-body systems by Monte Carlo methods, which is termed the Analytical Continuation Problem.'' For the Anderson model of dilute magnetic impurities in metals, we obtain spectral functions and transport coefficients which obey Kondo Universality.'' 24 refs., 7 figs.

  12. Discovering correlated fermions using quantum Monte Carlo.

    PubMed

    Wagner, Lucas K; Ceperley, David M

    2016-09-01

    It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior. PMID:27518859

  13. Discovering correlated fermions using quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Wagner, Lucas K.; Ceperley, David M.

    2016-09-01

    It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.

  14. Quantum Monte Carlo calculations of light nuclei.

    SciTech Connect

    Pieper, S. C.; Physics

    2008-01-01

    Variational Monte Carlo and Green's function Monte Carlo are powerful tools for cal- culations of properties of light nuclei using realistic two-nucleon (NN) and three-nucleon (NNN) potentials. Recently the GFMC method has been extended to multiple states with the same quantum numbers. The combination of the Argonne v18 two-nucleon and Illinois-2 three-nucleon potentials gives a good prediction of many energies of nuclei up to 12 C. A number of other recent results are presented: comparison of binding energies with those obtained by the no-core shell model; the incompatibility of modern nuclear Hamiltonians with a bound tetra-neutron; difficulties in computing RMS radii of very weakly bound nuclei, such as 6He; center-of-mass effects on spectroscopic factors; and the possible use of an artificial external well in calculations of neutron-rich isotopes.

  15. Quantum Monte Carlo calculations for carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Luu, Thomas; Lähde, Timo A.

    2016-04-01

    We show how lattice quantum Monte Carlo can be applied to the electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. Our lattice Hamiltonian is closely related to the hexagonal Hubbard model augmented by a long-range electron-electron interaction. We apply our method to the single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and consider the effects of strong electron-electron correlations. Our approach is equally applicable to other nanotubes, as well as to other carbon nanostructures. We benchmark our Monte Carlo calculations against the two- and four-site Hubbard models, where a direct numerical solution is feasible.

  16. Quantum Monte Carlo calculations for light nuclei.

    SciTech Connect

    Wiringa, R. B.

    1998-10-23

    Quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A {le} 8 are made using a realistic Hamiltonian that fits NN scattering data. Results for more than 40 different (J{pi}, T) states, plus isobaric analogs, are obtained and the known excitation spectra are reproduced reasonably well. Various density and momentum distributions and electromagnetic form factors and moments have also been computed. These are the first microscopic calculations that directly produce nuclear shell structure from realistic NN interactions.

  17. Quantum Monte Carlo for vibrating molecules

    SciTech Connect

    Brown, W.R. |

    1996-08-01

    Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H{sub 2}O and C{sub 3} vibrational states, using 7 PES`s, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H{sub 2}O and C{sub 3}. In order to construct accurate trial wavefunctions for C{sub 3}, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C{sub 3} the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C{sub 3} PES`s suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies.

  18. Quantum Monte Carlo methods for nuclear physics

    SciTech Connect

    Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.

    2015-09-01

    Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. Furthermore, a coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

  19. Quantum Monte Carlo methods for nuclear physics

    DOE PAGESBeta

    Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.

    2015-09-01

    Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit,more » and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. Furthermore, a coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less

  20. Quantum Monte Carlo methods for nuclear physics

    DOE PAGESBeta

    Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; Pieper, Steven C.; Schiavilla, Rocco; Schmidt, K. E,; Wiringa, Robert B.

    2014-10-19

    Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-bodymore » interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less

  1. Metallic lithium by quantum Monte Carlo

    SciTech Connect

    Sugiyama, G.; Zerah, G.; Alder, B.J.

    1986-12-01

    Lithium was chosen as the simplest known metal for the first application of quantum Monte Carlo methods in order to evaluate the accuracy of conventional one-electron band theories. Lithium has been extensively studied using such techniques. Band theory calculations have certain limitations in general and specifically in their application to lithium. Results depend on such factors as charge shape approximations (muffin tins), pseudopotentials (a special problem for lithium where the lack of rho core states requires a strong pseudopotential), and the form and parameters chosen for the exchange potential. The calculations are all one-electron methods in which the correlation effects are included in an ad hoc manner. This approximation may be particularly poor in the high compression regime, where the core states become delocalized. Furthermore, band theory provides only self-consistent results rather than strict limits on the energies. The quantum Monte Carlo method is a totally different technique using a many-body rather than a mean field approach which yields an upper bound on the energies. 18 refs., 4 figs., 1 tab.

  2. Chemical application of diffusion quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Reynolds, P. J.; Lester, W. A., Jr.

    1983-10-01

    The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. As an example the singlet-triplet splitting of the energy of the methylene molecule CH2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on our VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX is discussed. Since CH2 has only eight electrons, most of the loops in this application are fairly short. The longest inner loops run over the set of atomic basis functions. The CPU time dependence obtained versus the number of basis functions is discussed and compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures. Finally, preliminary work on restructuring the algorithm to compute the separate Monte Carlo realizations in parallel is discussed.

  3. Quantum Monte Carlo methods for nuclear physics

    SciTech Connect

    Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.

    2015-09-09

    Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. Furthermore, a coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

  4. Quantum Monte Carlo methods for nuclear physics

    SciTech Connect

    Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; Pieper, Steven C.; Schiavilla, Rocco; Schmidt, K. E,; Wiringa, Robert B.

    2014-10-19

    Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

  5. Noncovalent Interactions by Quantum Monte Carlo.

    PubMed

    Dubecký, Matúš; Mitas, Lubos; Jurečka, Petr

    2016-05-11

    Quantum Monte Carlo (QMC) is a family of stochastic methods for solving quantum many-body problems such as the stationary Schrödinger equation. The review introduces basic notions of electronic structure QMC based on random walks in real space as well as its advances and adaptations to systems with noncovalent interactions. Specific issues such as fixed-node error cancellation, construction of trial wave functions, and efficiency considerations that allow for benchmark quality QMC energy differences are described in detail. Comprehensive overview of articles covers QMC applications to systems with noncovalent interactions over the last three decades. The current status of QMC with regard to efficiency, applicability, and usability by nonexperts together with further considerations about QMC developments, limitations, and unsolved challenges are discussed as well. PMID:27081724

  6. Chemical application of diffusion quantum Monte Carlo

    NASA Technical Reports Server (NTRS)

    Reynolds, P. J.; Lester, W. A., Jr.

    1984-01-01

    The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.

  7. Novel Quantum Monte Carlo Approaches for Quantum Liquids

    NASA Astrophysics Data System (ADS)

    Rubenstein, Brenda M.

    Quantum Monte Carlo methods are a powerful suite of techniques for solving the quantum many-body problem. By using random numbers to stochastically sample quantum properties, QMC methods are capable of studying low-temperature quantum systems well beyond the reach of conventional deterministic techniques. QMC techniques have likewise been indispensible tools for augmenting our current knowledge of superfluidity and superconductivity. In this thesis, I present two new quantum Monte Carlo techniques, the Monte Carlo Power Method and Bose-Fermi Auxiliary-Field Quantum Monte Carlo, and apply previously developed Path Integral Monte Carlo methods to explore two new phases of quantum hard spheres and hydrogen. I lay the foundation for a subsequent description of my research by first reviewing the physics of quantum liquids in Chapter One and the mathematics behind Quantum Monte Carlo algorithms in Chapter Two. I then discuss the Monte Carlo Power Method, a stochastic way of computing the first several extremal eigenvalues of a matrix too memory-intensive to be stored and therefore diagonalized. As an illustration of the technique, I demonstrate how it can be used to determine the second eigenvalues of the transition matrices of several popular Monte Carlo algorithms. This information may be used to quantify how rapidly a Monte Carlo algorithm is converging to the equilibrium probability distribution it is sampling. I next present the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm. This algorithm generalizes the well-known Auxiliary-Field Quantum Monte Carlo algorithm for fermions to bosons and Bose-Fermi mixtures. Despite some shortcomings, the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm represents the first exact technique capable of studying Bose-Fermi mixtures of any size in any dimension. In Chapter Six, I describe a new Constant Stress Path Integral Monte Carlo algorithm for the study of quantum mechanical systems under high pressures. While

  8. Quantum Monte Carlo Endstation for Petascale Computing

    SciTech Connect

    Lubos Mitas

    2011-01-26

    NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13

  9. Quantum Monte Carlo for atoms and molecules

    SciTech Connect

    Barnett, R.N.

    1989-11-01

    The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H{sub 2}, LiH, Li{sub 2}, and H{sub 2}O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li{sub 2}, and H{sub 2}O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations, the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions.

  10. Computing Entanglement Entropy in Quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Melko, Roger

    2012-02-01

    The scaling of entanglement entropy in quantum many-body wavefunctions is expected to be a fruitful resource for studying quantum phases and phase transitions in condensed matter. However, until the recent development of estimators for Renyi entropy in quantum Monte Carlo (QMC), we have been in the dark about the behaviour of entanglement in all but the simplest two-dimensional models. In this talk, I will outline the measurement techniques that allow access to the Renyi entropies in several different QMC methodologies. I will then discuss recent simulation results demonstrating the richness of entanglement scaling in 2D, including: the prevalence of the ``area law''; topological entanglement entropy in a gapped spin liquid; anomalous subleading logarithmic terms due to Goldstone modes; universal scaling at critical points; and examples of emergent conformal-like scaling in several gapless wavefunctions. Finally, I will explore the idea that ``long range entanglement'' may complement the notion of ``long range order'' for quantum phases and phase transitions which lack a conventional order parameter description.

  11. Quantum Monte Carlo simulations in novel geometries

    NASA Astrophysics Data System (ADS)

    Iglovikov, Vladimir

    Quantum Monte Carlo simulations are giving increasing insight into the physics of strongly interacting bosons, spins, and fermions. Initial work focused on the simplest geometries, like a 2D square lattice. Increasingly, modern research is turning to more rich structures such as honeycomb lattice of graphene, the Lieb lattice of the CuO2 planes of cuprate superconductors, the triangular lattice, and coupled layers. These new geometries possess unique features which affect the physics in profound ways, eg a vanishing density of states and relativistic dispersion ("Dirac point'') of a honeycomb lattice, frustration on a triangular lattice, and a flat bands on a Lieb lattice. This thesis concerns both exploring the performance of QMC algorithms on different geometries(primarily via the "sign problem'') and also applying those algorithms to several interesting open problems.

  12. Optimized trial functions for quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Huang, Sheng-Yu; Sun, Zhiwei; Lester, William A., Jr.

    1990-01-01

    An algorithm to optimize trial functions for fixed-node quantum Monte Carlo calculations has been developed based on variational random walks. The approach is applied to wave functions that are products of a simple Slater determinant and correlation factor explicitly dependent on interelectronic distance, and is found to provide improved ground-state total energies. A modification of the method for ground-states that makes use of a projection operator technique is shown to make possible the calculation of more accurate excited-state energies. In this optimization method the Young tableaux of the permutation group is used to facilitate the treatment of fermion properties and multiplets. Application to ground states of H2, Li2, H3, H+3, and to the first-excited singlets of H2, H3, and H4 are presented and discussed.

  13. Optimized trial functions for quantum Monte Carlo

    SciTech Connect

    Huang, S.; Sun, Z.; Lester, W.A. Jr. )

    1990-01-01

    An algorithm to optimize trial functions for fixed-node quantum Monte Carlo calculations has been developed based on variational random walks. The approach is applied to wave functions that are products of a simple Slater determinant and correlation factor explicitly dependent on interelectronic distance, and is found to provide improved ground-state total energies. A modification of the method for ground-states that makes use of a projection operator technique is shown to make possible the calculation of more accurate excited-state energies. In this optimization method the Young tableaux of the permutation group is used to facilitate the treatment of fermion properties and multiplets. Application to ground states of H{sub 2}, Li{sub 2}, H{sub 3}, H{sup +}{sub 3}, and to the first-excited singlets of H{sub 2}, H{sub 3}, and H{sub 4} are presented and discussed.

  14. Quantum Monte Carlo : not just for energy levels.

    SciTech Connect

    Nollett, K. M.; Physics

    2007-01-01

    Quantum Monte Carlo and realistic interactions can provide well-motivated vertices and overlaps for DWBA analyses of reactions. Given an interaction in vaccum, there are several computational approaches to nuclear systems, as you have been hearing: No-core shell model with Lee-Suzuki or Bloch-Horowitz for Hamiltonian Coupled clusters with G-matrix interaction Density functional theory, granted an energy functional derived from the interaction Quantum Monte Carlo - Variational Monte Carlo Green's function Monte Carlo. The last two work directly with a bare interaction and bare operators and describe the wave function without expanding in basis functions, so they have rather different sets of advantages and disadvantages from the others. Variational Monte Carlo (VMC) is built on a sophisticated Ansatz for the wave function, built on shell model like structure modified by operator correlations. Green's function Monte Carlo (GFMC) uses an operator method to project the true ground state out of a reasonable guess wave function.

  15. Theory and Applications of Quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Deible, Michael John

    With the development of peta-scale computers and exa-scale only a few years away, the quantum Monte Carlo (QMC) method, with favorable scaling and inherent parrallelizability, is poised to increase its impact on the electronic structure community. The most widely used variation of QMC is the diffusion Monte Carlo (DMC) method. The accuracy of the DMC method is only limited by the trial wave function that it employs. The effect of the trial wave function is studied here by initially developing correlation-consistent Gaussian basis sets for use in DMC calculations. These basis sets give a low variance in variance Monte Carlo calculations and improved convergence in DMC. The orbital type used in the trial wave function is then investigated, and it is shown that Brueckner orbitals result in a DMC energy comparable to a DMC energy with orbitals from density functional theory and significantly lower than orbitals from Hartree-Fock theory. Three large weakly interacting systems are then studied; a water-16 isomer, a methane clathrate, and a carbon dioxide clathrate. The DMC method is seen to be in good agreement with MP2 calculations and provides reliable benchmarks. Several strongly correlated systems are then studied. An H4 model system that allows for a fine tuning of the multi-configurational character of the wave function shows when the accuracy of the DMC method with a single Slater-determinant trial function begins to deviate from multi-reference benchmarks. The weakly interacting face-to-face ethylene dimer is studied with and without a rotation around the pi bond, which is used to increase the multi-configurational nature of the wave function. This test shows that the effect of a multi-configurational wave function in weakly interacting systems causes DMC with a single Slater-determinant to be unable to achieve sub-chemical accuracy. The beryllium dimer is studied, and it is shown that a very large determinant expansion is required for DMC to predict a binding

  16. Linear Scaling Quantum Monte Carlo Calculations

    NASA Astrophysics Data System (ADS)

    Williamson, Andrew

    2002-03-01

    New developments to the quantum Monte Carlo approach are presented that improve the scaling of the time required to calculate the total energy of a configuration of electronic coordinates from N^3 to nearly linear[1]. The first factor of N is achieved by applying a unitary transform to the set of single particle orbitals used to construct the Slater determinant, creating a set of maximally localized Wannier orbitals. These localized functions are then truncated beyond a given cutoff radius to introduce sparsity into the Slater determinant. The second factor of N is achieved by evaluating the maximally localized Wannier orbitals on a cubic spline grid, which removes the size dependence of the basis set (e.g. plane waves, Gaussians) typically used to expand the orbitals. Application of this method to the calculation of the binding energy of carbon fullerenes and silicon nanostructures will be presented. An extension of the approach to deal with excited states of systems will also be presented in the context of the calculation of the excitonic gap of a variety of systems. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/LLNL under contract no. W-7405-Eng-48. [1] A.J. Williamson, R.Q. Hood and J.C. Grossman, Phys. Rev. Lett. 87 246406 (2001)

  17. Quantum Monte Carlo calculations on positronium compounds

    NASA Astrophysics Data System (ADS)

    Jiang, Nan

    The stability of compounds containing one or more positrons in addition to electrons and nuclei has been the focus of extensive scientific investigations. Interest in these compounds stems from the important role they play in the process of positron annihilation, which has become a useful technique in material science studies. Knowledge of these compounds comes mostly from calculations which are presently less difficult than laboratory experiments. Owing to the small binding energies of these compounds, quantum chemistry methods beyond the molecular orbital approximation must be used. Among them, the quantum Monte Carlo (QMC) method is most appealing because it is easy to implement, gives exact results within the fixed nodes approximation, and makes good use of existing approximate wavefunctions. Applying QMC to small systems like PsH for binding energy calculation is straightforward. To apply it to systems with heavier atoms, to systems for which the center-of-mass motion needs to be separated, and to calculate annihilation rates, special techniques must be developed. In this project a detailed study and several advancements to the QMC method are carried out. Positronium compounds PsH, Ps2, PsO, and Ps2O are studied with algorithms we developed. Results for PsH and Ps2 agree with the best accepted to date. Results for PsO confirm the stability of this compound, and are in fair agreement with an earlier calculation. Results for Ps2O establish the stability of this compound and give an approximate annihilation rate for the first time. Discussions will include an introduction to QMC methods, an in-depth discussion on the QMC formalism, presentation of new algorithms developed in this study, and procedures and results of QMC calculations on the above mentioned positronium compounds.

  18. Quantum Monte Carlo Endstation for Petascale Computing

    SciTech Connect

    David Ceperley

    2011-03-02

    CUDA GPU platform. We restructured the CPU algorithms to express additional parallelism, minimize GPU-CPU communication, and efficiently utilize the GPU memory hierarchy. Using mixed precision on GT200 GPUs and MPI for intercommunication and load balancing, we observe typical full-application speedups of approximately 10x to 15x relative to quad-core Xeon CPUs alone, while reproducing the double-precision CPU results within statistical error. We developed an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and used it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We computed the static contribution to the free energy with the QMC method and obtained the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We computed the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy. We compared experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derived its discontinuity at the Fermi wavevector finding an accurate measure of the renormalization factor that we compared with quantum-Monte-Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment. We have been studying the heat of formation for various Kubas complexes of molecular

  19. Understanding Quantum Tunneling through Quantum Monte Carlo Simulations

    NASA Astrophysics Data System (ADS)

    Boixo, Sergio; Isakov, Sergei; Mazzola, Guglielmo; Smelyanskiy, Vadim; Jiang, Zhang; Neven, Hartmut; Troyer, Matthias

    The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling (in the exponent) with system size, as the rate of incoherent tunneling. The scaling in both cases is O (Δ2) , where Δ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture.

  20. Quantum Monte Carlo studies on small molecules

    NASA Astrophysics Data System (ADS)

    Galek, Peter T. A.; Handy, Nicholas C.; Lester, William A., Jr.

    The Variational Monte Carlo (VMC) and Fixed-Node Diffusion Monte Carlo (FNDMC) methods have been examined, through studies on small molecules. New programs have been written which implement the (by now) standard algorithms for VMC and FNDMC. We have employed and investigated throughout our studies the accuracy of the common Slater-Jastrow trial wave function. Firstly, we have studied a range of sizes of the Jastrow correlation function of the Boys-Handy form, obtained using our optimization program with analytical derivatives of the central moments in the local energy. Secondly, we have studied the effects of Slater-type orbitals (STOs) that display the exact cusp behaviour at nuclei. The orbitals make up the all important trial determinant, which determines the fixed nodal surface. We report all-electron calculations for the ground state energies of Li2, Be2, H2O, NH3, CH4 and H2CO, in all cases but one with accuracy in excess of 95%. Finally, we report an investigation of the ground state energies, dissociation energies and ionization potentials of NH and NH+. Recent focus paid in the literature to these species allow for an extensive comparison with other ab initio methods. We obtain accurate properties for the species and reveal a favourable tendency for fixed-node and other systematic errors to cancel. As a result of our accurate predictions, we are able to obtain a value for the heat of formation of NH, which agrees to within less than 1 kcal mol-1 to other ab initio techniques and 0.2 kcal mol-1 of the experimental value.

  1. Monte Carlo techniques for real-time quantum dynamics

    SciTech Connect

    Dowling, Mark R. . E-mail: dowling@physics.uq.edu.au; Davis, Matthew J.; Drummond, Peter D.; Corney, Joel F.

    2007-01-10

    The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the 'weight', and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.

  2. Monte Carlo studies of nuclei and quantum liquid drops

    SciTech Connect

    Pandharipande, V.R.; Pieper, S.C.

    1989-01-01

    The progress in application of variational and Green's function Monte Carlo methods to nuclei is reviewed. The nature of single-particle orbitals in correlated quantum liquid drops is discussed, and it is suggested that the difference between quasi-particle and mean-field orbitals may be of importance in nuclear structure physics. 27 refs., 7 figs., 2 tabs.

  3. Reagents for Electrophilic Amination: A Quantum Monte CarloStudy

    SciTech Connect

    Amador-Bedolla, Carlos; Salomon-Ferrer, Romelia; Lester Jr.,William A.; Vazquez-Martinez, Jose A.; Aspuru-Guzik, Alan

    2006-11-01

    Electroamination is an appealing synthetic strategy toconstruct carbon-nitrogen bonds. We explore the use of the quantum MonteCarlo method and a proposed variant of the electron-pair localizationfunction--the electron-pair localization function density--as a measureof the nucleophilicity of nitrogen lone-pairs as a possible screeningprocedure for electrophilic reagents.

  4. Quantum Monte Carlo simulation with a black hole

    NASA Astrophysics Data System (ADS)

    Benić, Sanjin; Yamamoto, Arata

    2016-05-01

    We perform quantum Monte Carlo simulations in the background of a classical black hole. The lattice discretized path integral is numerically calculated in the Schwarzschild metric and in its approximated metric. We study spontaneous symmetry breaking of a real scalar field theory. We observe inhomogeneous symmetry breaking induced by an inhomogeneous gravitational field.

  5. Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

    NASA Technical Reports Server (NTRS)

    Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

    2015-01-01

    Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

  6. Chemical accuracy from quantum Monte Carlo for the benzene dimer

    SciTech Connect

    Azadi, Sam; Cohen, R. E.

    2015-09-14

    We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

  7. Chemical accuracy from quantum Monte Carlo for the benzene dimer.

    PubMed

    Azadi, Sam; Cohen, R E

    2015-09-14

    We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods. PMID:26374029

  8. Monte Carlo simulation of quantum Zeno effect in the brain

    NASA Astrophysics Data System (ADS)

    Georgiev, Danko

    2015-12-01

    Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved a theorem according to which local projections cannot decrease the von Neumann entropy of the unconditional brain density matrix. The latter theorem establishes that Stapp's model is physically implausible but leaves a door open for future development of quantum mind theories provided the brain has a decoherence-free subspace.

  9. Energies of the first row atoms from quantum Monte Carlo.

    PubMed

    Brown, M D; Trail, J R; Ríos, P López; Needs, R J

    2007-06-14

    All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusion quantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlation energies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F. PMID:17581047

  10. Quantum Monte Carlo Simulation of Tunneling Devices Using Bohm Trajectories

    NASA Astrophysics Data System (ADS)

    Oriols, X.; García-García, J. J.; Martín, F.; Suñé, J.; González, T.; Mateos, J.; Pardo, D.

    1997-11-01

    A generalization of the classical Monte Carlo (MC) device simulation technique is proposed to simultaneously deal with quantum-mechanical phase-coherence effects and scattering interactions in tunneling devices. The proposed method restricts the quantum treatment of transport to the regions of the device where the potential profile significantly changes in distances of the order of the de Broglie wavelength of the carriers (the quantum window). Bohm trajectories associated to time-dependent Gaussian wavepackets are used to simulate the electron transport in the quantum window. Outside this window, the classical ensemble simulation technique is used. Classical and quantum trajectories are smoothly matched at the boundaries of the quantum window according to a criterium of total energy conservation. A simple one-dimensional simulator for resonant tunneling diodes is presented to demonstrate the feasibility of our proposal.

  11. Valence-bond quantum Monte Carlo algorithms defined on trees.

    PubMed

    Deschner, Andreas; Sørensen, Erik S

    2014-09-01

    We present a class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a projective T=0 Monte Carlo method based on sampling of a set of operator strings that can be viewed as forming a treelike structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator string. In quite general terms, we derive a set of equations whose solutions correspond to a whole class of algorithms. As specific examples of this class of algorithms, we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree, and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update. PMID:25314561

  12. Semi-stochastic full configuration interaction quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Holmes, Adam; Petruzielo, Frank; Khadilkar, Mihir; Changlani, Hitesh; Nightingale, M. P.; Umrigar, C. J.

    2012-02-01

    In the recently proposed full configuration interaction quantum Monte Carlo (FCIQMC) [1,2], the ground state is projected out stochastically, using a population of walkers each of which represents a basis state in the Hilbert space spanned by Slater determinants. The infamous fermion sign problem manifests itself in the fact that walkers of either sign can be spawned on a given determinant. We propose an improvement on this method in the form of a hybrid stochastic/deterministic technique, which we expect will improve the efficiency of the algorithm by ameliorating the sign problem. We test the method on atoms and molecules, e.g., carbon, carbon dimer, N2 molecule, and stretched N2. [4pt] [1] Fermion Monte Carlo without fixed nodes: a Game of Life, death and annihilation in Slater Determinant space. George Booth, Alex Thom, Ali Alavi. J Chem Phys 131, 050106, (2009).[0pt] [2] Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo. Deidre Cleland, George Booth, and Ali Alavi. J Chem Phys 132, 041103 (2010).

  13. Minimising biases in full configuration interaction quantum Monte Carlo.

    PubMed

    Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W

    2015-03-14

    We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to, in general, minimise the bias. We show a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo [Umrigar et al., J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step. PMID:25770522

  14. Continuous-time quantum Monte Carlo impurity solvers

    NASA Astrophysics Data System (ADS)

    Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias

    2011-04-01

    Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as

  15. Performance of quantum Monte Carlo for calculating molecular bond lengths

    NASA Astrophysics Data System (ADS)

    Cleland, Deidre M.; Per, Manolo C.

    2016-03-01

    This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10-3 Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10-3 Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

  16. Quantum Monte Carlo theory and applications for molecular systems

    NASA Astrophysics Data System (ADS)

    Kollias, Alexander C.

    New directions for the quantum Monte Carlo (QMC) electronic structure method are discussed. Diffusion Monte Carlo (DMC) results for the atomization energy and heats for formation of CO+2 are presented, while the bonding character is examined using the electron localization function. DMC all-electron and effective-core potential trial functions are used to obtain the atomization energies, heats of formation, and energy differences of the C2H4 singlet and triplet states. In addition, DMC is applied to obtain the heat of reaction and barrier height of the proton extraction reaction, CH3OH + Cl → CH 2OH + HCl. The results of the barrier height and heat of reaction are verified by examining the atomization energies and heats for formation of the reactants and products. DMC calculations were carried out on 22 small hydrocarbons. In this benchmark study the DMC atomization and bond dissociation energies, and heats of formation of these hydrocarbons are presented and compared to other ab initio methods. Methods for geometry optimization and calculating forces for QMC are discussed. The response surface methodology is applied to variational Monte Carlo (VMC) and DMC methods to obtain an optimized geometry, force constants and vibrational frequencies of CH2O. Finally, the zero-variance principle is applied to obtain VMC and DMC effective-core potential force estimators. These estimators are used to obtain a force curve for LiH.

  17. Infinite variance in fermion quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Shi, Hao; Zhang, Shiwei

    2016-03-01

    For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

  18. Constrained Path Quantum Monte Carlo Method for Fermion Ground States

    NASA Astrophysics Data System (ADS)

    Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.

    1995-05-01

    We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wave function by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wave function \\|ΨT>, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \\|ΨT> is exact. We report results on the two-dimensional Hubbard model up to size 16×16, for various electron fillings and interaction strengths.

  19. Monte Carlo simulation of a noisy quantum channel with memory.

    PubMed

    Akhalwaya, Ismail; Moodley, Mervlyn; Petruccione, Francesco

    2015-10-01

    The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision. PMID:26565361

  20. Properties of reactive oxygen species by quantum Monte Carlo

    SciTech Connect

    Zen, Andrea; Trout, Bernhardt L.; Guidoni, Leonardo

    2014-07-07

    The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N{sup 3} − N{sup 4}, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.

  1. Properties of reactive oxygen species by quantum Monte Carlo.

    PubMed

    Zen, Andrea; Trout, Bernhardt L; Guidoni, Leonardo

    2014-07-01

    The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N(3) - N(4), where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles. PMID:25005287

  2. Properties of reactive oxygen species by quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Zen, Andrea; Trout, Bernhardt L.; Guidoni, Leonardo

    2014-07-01

    The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N3 - N4, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.

  3. Quantum Monte Carlo calculations of {Alpha} = 8 nuclei.

    SciTech Connect

    Wiringa, R. B.; Pieper, S. C.; Carlson, J.; Pandharipande, V. R.; Physics; LANL; Univ. of Illinois

    2000-07-01

    We report quantum Monte Carlo calculations of ground and low-lying excited states for {Alpha}=8 nuclei using a realistic Hamiltonian containing the Argonne v{sub 18} two-nucleon and Urbana IX three-nucleon potentials. The calculations begin with correlated eight-body wave functions that have a filled {alpha}-like core and four p-shell nucleons LS coupled to the appropriate (J{sup {pi}},T) quantum numbers for the state of interest. After optimization, these variational wave functions are used as input to a Green's function Monte Carlo calculation made with a new constrained path algorithm. We find that the Hamiltonian produces a {sup 8}Be ground state that is within 2 MeV of the experimental resonance, but the other eight-body energies are progressively worse as the neutron-proton asymmetry increases. The {sup 8}Li ground state is stable against breakup into subclusters, but the {sup 8}He ground state is not. The excited state spectra are in fair agreement with experiment, with both the single-particle behavior of {sup 8}He and {sup 8}Li and the collective rotational behavior of {sup 8}Be being reproduced. We also examine energy differences in the T=1,2 isomultiplets and isospin-mixing matrix elements in the excited states of {sup 8}Be. Finally, we present densities, momentum distributions, and studies of the intrinsic shapes of these nuclei, with {sup 8}Be exhibiting a definite 2{alpha} cluster structure.

  4. A pure-sampling quantum Monte Carlo algorithm

    SciTech Connect

    Ospadov, Egor; Rothstein, Stuart M.

    2015-01-14

    The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.

  5. Variational quantum Monte Carlo calculations for solid surfaces

    SciTech Connect

    Bahnsen, R.; Eckstein, H.; Schattke, W.; Fitzer, N.; Redmer, R.

    2001-06-15

    Quantum Monte Carlo methods have proven to predict atomic and bulk properties of light and nonlight elements with high accuracy. Here we report on variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking the boundary condition for the simulation from a finite-layer geometry, the Hamiltonian, including a nonlocal pseudopotential, is cast in a layer-resolved form and evaluated with a two-dimensional Ewald summation technique. The exact cancellation of all jellium contributions to the Hamiltonian is ensured. The many-body trial wave function consists of a Slater determinant with parametrized localized orbitals and a Jastrow factor with a common two-body term plus an additional confinement term representing further variational freedom to take into account the existence of the surface. We present results for the ideal (110) surface of gallium arsenide for different system sizes. With the optimized trial wave function, we determine some properties related to a solid surface to illustrate that VMC techniques provide reasonable results under full inclusion of many-body effects at solid surfaces.

  6. Spinor path integral Quantum Monte Carlo for fermions

    NASA Astrophysics Data System (ADS)

    Shin, Daejin; Yousif, Hosam; Shumway, John

    2007-03-01

    We have developed a continuous-space path integral method for spin 1/2 fermions with fixed-phase approximation. The internal spin degrees of freedom of each particle is represented by four extra dimensions. This effectively maps each spinor onto two of the excited states of a four dimensional harmonic oscillator. The phases that appear in the problem can be treated within the fixed-phase approximation. This mapping preserves rotational invariance and allows us to treat spin interactions and fermionic exchange on equal footing, which may lead to new theoretical insights. The technique is illustrated for a few simple models, including a spin in a magnetic field and interacting electrons in a quantum dot in a magnetic field at finite temperature. We will discuss possible extensions of the method to molecules and solids using variational and diffusion Quantum Monte Carlo.

  7. Quantum Monte Carlo simulations with tensor-network states

    NASA Astrophysics Data System (ADS)

    Song, Jeong Pil; Clay, R. T.

    2011-03-01

    Matrix-product states, generated by the density-matrix renormalization group method, are among the most powerful methods for simulation of quasi-one dimensional quantum systems. Direct application of a matrix-product state representation fails for two dimensional systems, although a number of tensor-network states have been proposed to generalize the concept for two dimensions. We introduce a useful approximate method replacing a 4-index tensor by two matrices in order to contract tensors in two dimensions. We use this formalism as a basis for variational quantum Monte Carlo, optimizing the matrix elements stochastically. We present results on a two dimensional spinless fermion model including nearest- neighbor Coulomb interactions, and determine the critical Coulomb interaction for the charge density wave state by finite size scaling. This work was supported by the Department of Energy grant DE-FG02-06ER46315.

  8. Correlated wavefunction quantum Monte Carlo approach to solids

    SciTech Connect

    Louie, S.G.

    1992-10-01

    A method for calculating the electronic and structural properties of solids using correlated wavefunctions together with quantum Monte Carlo techniques is described. The approach retains the exact Coulomb interaction between the electrons and employs a many-electron wavefunction of the Jastrow-Slater form. Several examples are given to illustrate the utility of the method. Topics discussed include the cohesive properties of bulk semiconductors, the magnetic-field- induced Wigner crystal in two dimensions, and the magnetic structure of bcc hydrogen. Landau level mixing is shown to be important in determining the transition between the fractional quantum Hall liquid and the Wigner crystal. Information on electron correlations such as the pair correlation functions which are not accessible to one- electron theories is also obtained. 24 refs, 5 figs, 1 tab.

  9. Two-Dimensional Ferromagnet: Quantum Monte Carlo results

    NASA Astrophysics Data System (ADS)

    Henelius, Patrik; Timm, Carsten; Girvin, Steven M.; Sandvik, Anders

    1997-03-01

    In the quantum Hall system the Zeeman interaction between electronic spins and the external magnetic field is typically weak compared to both the Landau-level splitting and the exchange interaction. Therefore, quantum Hall systems at integer filling factors can be ferromagnets. The magnetization and, recently, the nuclear magnetic relaxation rate 1/T1 have been measured for these magnets.(S.E. Barrett et al.), Phys. Rev. Lett. 72, 1368 (1994); 74, 5112 (1995) These quantities have been calculated in a Schwinger-boson mean-field approach.(N. Read and S. Sachdev, Phys. Rev. Lett. 75), 3509 (1995) We have calculated these same quantities using a Stochastic Series Expansion Monte Carlo Method. The results are compared with the experimental data, the mean-field results and with 1/N corrections for the mean-field results, calculated by our group.

  10. Fast evaluation of multideterminant wavefunctions in quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Morales, Miguel A.; Clark, Bryan K.; McMinis, Jeremy; Kim, Jeongnim; Scuseria, Gustavo

    2011-03-01

    Quantum Monte Carlo (QMC) methods such as variational and diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multislater- Jastrow wave function which consists of a Jastrow function multiplied by the sum of slater determinants. In this talk we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient, and easily parallelized. The algorithm computes the multi determinant ratios of a series of particle hole excitations in time O(n 2) + O(n s n)+O(n e) where n, n s and n e are the number of particles, single particle excitations, and total number of excitations, respectively. This is accomplished by producing a (relatively) compact table that contains all the information required to read off the excitation ratios. In addition we describe how to compute the gradients and laplacians of these multi determinant terms. This work was performed under the auspices of: the US DOE by LLNL under Contract DE-AC52-07NA27344, the US DOE under Contract DOE-DE-FG05-08OR23336 and by NSF under No.0904572.

  11. Quantum Monte Carlo Simulations of Correlated-Electron Models

    NASA Astrophysics Data System (ADS)

    Zhang, Shiwei

    1996-05-01

    We briefly review quantum Monte Carlo simulation methods for strongly correlated fermion systems and the well-known ``sign'' problem that plagues these methods. We then discuss recent efforts to overcome the problem in the context of simulations of lattice models of electron correlations. In particular, we describe a new algorithm^1, called the constrained path Monte Carlo (CPMC), for studying ground-state (T=0K) properties. It has the form of a random walk in a space of mean-field solutions (Slater determinants); the exponential decay of ``sign'' or signal-to-noise ratio is eliminated by constraining the paths of the random walk according to a known trial wave function. Applications of this algorithm to the Hubbard model have enabled accurate and systematic studies of correlation functions, including s- and d-wave pairings, and hence the long-standing problem of the model's relevance to superconductivity. The method is directly applicable to a variety of other models important to understand high-Tc superconductors and heavy-fermion compounds. In addition, it is expected to be useful to simulations of nuclei, atoms, molecules, and solids. We also comment on possible extensions of the algorithm to finite-temperature calculations. Work supported in part by the Department of Energy's High Performance Computing and Communication Program at Los Alamos National Laboratory, and at OSU by DOE-Basic Energy Sciences, Division of Materials Sciences. ^1 Shiwei Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. Lett. 74, 3652 (1995).

  12. Quantum Monte Carlo Calculations of Nucleon-Nucleus Scattering

    NASA Astrophysics Data System (ADS)

    Wiringa, R. B.; Nollett, Kenneth M.; Pieper, Steven C.; Brida, I.

    2009-10-01

    We report recent quantum Monte Carlo (variational and Green's function) calculations of elastic nucleon-nucleus scattering. We are adding the cases of proton-^4He, neutron-^3H and proton-^3He scattering to a previous GFMC study of neutron-^4He scattering [1]. To do this requires generalizing our methods to include long-range Coulomb forces and to treat coupled channels. The two four-body cases can be compared to other accurate four-body calculational methods such as the AGS equations and hyperspherical harmonic expansions. We will present results for the Argonne v18 interaction alone and with Urbana and Illinois three-nucleon potentials. [4pt] [1] K.M. Nollett, S. C. Pieper, R.B. Wiringa, J. Carlson, and G.M. Hale, Phys. Rev. Lett. 99, 022502 (2007)

  13. Quantum states of confined hydrogen plasma species: Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Micca Longo, G.; Longo, S.; Giordano, D.

    2015-12-01

    The diffusion Monte Carlo method with symmetry-based state selection is used to calculate the quantum energy states of \\text{H}2+ confined into potential barriers of atomic dimensions (a model for these ions in solids). Special solutions are employed, permitting one to obtain satisfactory results with rather simple native code. As a test case, {{}2}{{\\Pi}u} and {{}2}{{\\Pi}g} states of \\text{H}2+ ions under spherical confinement are considered. The results are interpreted using the correlation of \\text{H}2+ states to atomic orbitals of H atoms lying on the confining surface and perturbation calculations. The method is straightforwardly applied to cavities of any shape and different hydrogen plasma species (at least one-electron ones, including H) for future studies with real crystal symmetries.

  14. Itinerant scenario for Fe pnictides: Comparison with quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Chubukov, Andrey V.; Xing, Rui-Qi

    2016-04-01

    Recent applications of quantum Monte Carlo (QMC) technique to Fe-based superconductors opened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper [arXiv:1512.08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. The type of the orbital order found in QMC is different from the one found in earlier itinerant analysis. We report the results of our calculations within the itinerant scenario and argue that they are in perfect agreement with QMC.

  15. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

    2015-06-01

    We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects.

  16. Quantum Monte Carlo study of bilayer ionic Hubbard model

    NASA Astrophysics Data System (ADS)

    Jiang, Mi

    The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for intermediate interaction U, which poses fundamental interest in the correlated electronic systems. Here we use determinant quantum Monte Carlo to study the interplay of interlayer hybridization V and two types of intralayer staggered potentials: one with the same (in-phase) and the other with a π-phase shift (anti-phase) potential in two layers termed as ``bilayer ionic Hubbard model''. We demonstrate that the interaction-driven Insulator-Metal transition extends to bilayer IHM with finite V for both types of staggered potentials. Besides, the system with in-phase potential is prone to metallic phase with turning on interlayer hybridization while that with anti-phase potential tends to insulators with stronger charge density order. The author thanks CSCS, Lugano, Switzerland for computing facilities.

  17. Quantum Monte Carlo study of bilayer ionic Hubbard model

    NASA Astrophysics Data System (ADS)

    Jiang, M.; Schulthess, T. C.

    2016-04-01

    The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction U , while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization V and two types of intralayer staggered potentials Δ : one with the same (in-phase) and the other with a π -phase shift (antiphase) potential between layers. Our determinant quantum Monte Carlo (DQMC) simulations at lowest accessible temperatures demonstrate that the interaction-driven metallic phase between Mott and band insulators expands in the Δ -V phase diagram of bilayer IHM only for in-phase ionic potentials; while antiphase potential always induces an insulator with charge density order. This implies possible further extension of the ionic Hubbard model from the bilayer case here to a realistic three-dimensional model.

  18. Quantum Monte Carlo for the Spectroscopy of Core Excited States

    NASA Astrophysics Data System (ADS)

    Zubarev, Dmitry

    2012-02-01

    X-ray absorption spectroscopy is a powerful experimental tool that is capable of delivering valuable information about very delicate aspects of electronic structure and reveals details of the local chemical environment in many systems of fundamental and applied importance. The rigorous interpretation of core-level spectra requires very accurate quantum chemical simulations. The trade-off between feasibility of treatment of large systems and consistency in description of electron correlation tremendously hinders the generation of accurate theoretical results for many experimental studies. We show that the fixed-node diffusion Monte Carlo (FN-DMC) approach can be used straightforwardly for the accurate simulation of core-level spectra. Basic methodological aspects are addressed, including the strategy for the construction of adequate trial wave functions. Examples of FN-DMC calculations of core-level spectra of water and pyrrole are presented. The possibility of the simulation of X-ray absorption spectra of solvent-solute systems is discussed.

  19. Continuous-time quantum Monte Carlo using worm sampling

    NASA Astrophysics Data System (ADS)

    Gunacker, P.; Wallerberger, M.; Gull, E.; Hausoel, A.; Sangiovanni, G.; Held, K.

    2015-10-01

    We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean-field theory and in efficient estimators for the single-particle self-energy.

  20. Quantum Monte Carlo study of magnetism in the Lieb Lattice

    NASA Astrophysics Data System (ADS)

    Costa, Natanael; Santos, Tiago; Paiva, Thereza; Dos Santos, Raimundo; Scalettar, Richard

    The Hubbard model on the `Lieb lattice' provides an important example of how flat band systems may lead to ferromagnetism: at half filling Lieb proved that a ferrimagnetic ground state can be achieved. Since a rigorous proof that long range order does indeed emerge is still lacking, here we report Determinant Quantum Monte Carlo (DQMC) simulations for this model. We found that the spin correlation between nearest neighbors are always antiferromagnetic, and that for small U ferromagnetic long range order does set in in the ground state. However, spatial spin correlations weaken as U is increased, and we established that long range order is suppressed above Uc ~ 4 . 5 . We obtain the dependence of the magnetization with the on-site repulsion U, and show that it displays a maximum at U ~ 3 . The behavior of the compressibility and of the double occupancy across this transition is also discussed. Also at Department of Physics, UC Davis.

  1. Quantum Monte Carlo calculations of A=8 nuclei

    SciTech Connect

    Wiringa, R. B.; Pieper, Steven C.; Carlson, J.; Pandharipande, V. R.

    2000-07-01

    We report quantum Monte Carlo calculations of ground and low-lying excited states for A=8 nuclei using a realistic Hamiltonian containing the Argonne v{sub 18} two-nucleon and Urbana IX three-nucleon potentials. The calculations begin with correlated eight-body wave functions that have a filled {alpha}-like core and four p-shell nucleons LS coupled to the appropriate (J{sup {pi}};T) quantum numbers for the state of interest. After optimization, these variational wave functions are used as input to a Green's function Monte Carlo calculation made with a new constrained path algorithm. We find that the Hamiltonian produces a {sup 8}Be ground state that is within 2 MeV of the experimental resonance, but the other eight-body energies are progressively worse as the neutron-proton asymmetry increases. The {sup 8}Li ground state is stable against breakup into subclusters, but the {sup 8}He ground state is not. The excited state spectra are in fair agreement with experiment, with both the single-particle behavior of {sup 8}He and {sup 8}Li and the collective rotational behavior of {sup 8}Be being reproduced. We also examine energy differences in the T=1,2 isomultiplets and isospin-mixing matrix elements in the excited states of {sup 8}Be. Finally, we present densities, momentum distributions, and studies of the intrinsic shapes of these nuclei, with {sup 8}Be exhibiting a definite 2{alpha} cluster structure. (c) 2000 The American Physical Society.

  2. Quantum Monte Carlo with very large multideterminant wavefunctions.

    PubMed

    Scemama, Anthony; Applencourt, Thomas; Giner, Emmanuel; Caffarel, Michel

    2016-07-01

    An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants,  Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc. PMID:27302337

  3. Quantum Monte Carlo Algorithms for Diagrammatic Vibrational Structure Calculations

    NASA Astrophysics Data System (ADS)

    Hermes, Matthew; Hirata, So

    2015-06-01

    Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as Møller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational Møller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.

  4. Pseudopotentials for quantum Monte Carlo studies of transition metal oxides

    NASA Astrophysics Data System (ADS)

    Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A.

    2016-02-01

    Quantum Monte Carlo (QMC) calculations of transition metal oxides are partially limited by the availability of high-quality pseudopotentials that are both accurate in QMC and compatible with major plane-wave electronic structure codes. We have generated a set of neon-core pseudopotentials with small cutoff radii for the early transition metal elements Sc to Zn within the local density approximation of density functional theory. The pseudopotentials have been directly tested for accuracy within QMC by calculating the first through fourth ionization potentials of the isolated transition metal (M) atoms and the binding curve of each M-O dimer. We find the ionization potentials to be accurate to 0.16(1) eV, on average, relative to experiment. The equilibrium bond lengths of the dimers are within 0.5(1)% of experimental values, on average, and the binding energies are also typically accurate to 0.18(3) eV. The level of accuracy we find for atoms and dimers is comparable to what has recently been observed for bulk metals and oxides using the same pseudopotentials. Our QMC pseudopotential results also compare well with the findings of previous QMC studies and benchmark quantum chemical calculations.

  5. Pseudopotentials for quantum Monte Carlo studies of transition metal oxides

    DOE PAGESBeta

    Krogel, Jaron T.; Santana Palacio, Juan A.; Reboredo, Fernando A.

    2016-02-22

    Quantum Monte Carlo (QMC) calculations of transition metal oxides are partially limited by the availability of high-quality pseudopotentials that are both accurate in QMC and compatible with major plane-wave electronic structure codes. We have generated a set of neon-core pseudopotentials with small cutoff radii for the early transition metal elements Sc to Zn within the local density approximation of density functional theory. The pseudopotentials have been directly tested for accuracy within QMC by calculating the first through fourth ionization potentials of the isolated transition metal (M) atoms and the binding curve of each M-O dimer. We find the ionization potentialsmore » to be accurate to 0.16(1) eV, on average, relative to experiment. The equilibrium bond lengths of the dimers are within 0.5(1)% of experimental values, on average, and the binding energies are also typically accurate to 0.18(3) eV. The level of accuracy we find for atoms and dimers is comparable to what has recently been observed for bulk metals and oxides using the same pseudopotentials. Our QMC pseudopotential results compare well with the findings of previous QMC studies and benchmark quantum chemical calculations.« less

  6. Generalized directed loop method for quantum Monte Carlo simulations.

    PubMed

    Alet, Fabien; Wessel, Stefan; Troyer, Matthias

    2005-03-01

    Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the nonuniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however, we find that the optimal strategy depends not only on the model parameters but also on the observable of interest. PMID:15903632

  7. Quantum Monte Carlo Calculations Applied to Magnetic Molecules

    SciTech Connect

    Larry Engelhardt

    2006-08-09

    We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations. The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these

  8. Quantum Monte Carlo calculations applied to magnetic molecules

    NASA Astrophysics Data System (ADS)

    Engelhardt, Larry Paul

    In this dissertation, we have implemented a quantum Monte Carlo (QMC) algorithm, and have used it to perform calculations for a variety of finite Heisenberg spin systems. A detailed description of the QMC method has been provided, which is followed by applications of the method to various systems. These applications begin with a detailed analysis of the (calculated) equilibrium magnetization and magnetic susceptibility for a number of Heisenberg Hamiltonians. In particular, we have studied the dependence of these quantities on intrinsic spin s, and have quantified the approach to the classical (s → infinity) limit. These results are not specific to a particular physical system, but are potentially applicable to many systems. We have also analyzed four recently synthesized species of magnetic molecules, each of which is theoretically challenging to the methods that are normally used for such analyses. Using the QMC method, we have distinguished the microscopic (exchange) parameters that describe the interactions in each of these magnetic molecules, and, based upon these parameters, we have made predictions for future experiments. The well-known "negative sign problem" (NSP) can be problematic for QMC calculations. However, for some systems, our analysis was able to proceed despite the NSP. For other systems, this is not the cases, so we have clearly indicated when the NSP is, and is not, insurmountable for these types of calculations.

  9. Quantum Monte Carlo investigations of adsorption energetics on graphene.

    PubMed

    Hsing, C R; Wei, C M; Chou, M Y

    2012-10-01

    We have performed calculations of adsorption energetics on the graphene surface using the state-of-the-art diffusion quantum Monte Carlo method. Two types of configurations are considered in this work: the adsorption of a single O, F, or H atom on the graphene surface and the H-saturated graphene system (graphane). The adsorption energies are compared with those obtained from density functional theory with various exchange-correlation functionals. The results indicate that the approximate exchange-correlation functionals significantly overestimate the binding of O and F atoms on graphene, although the preferred adsorption sites are consistent. The energy errors are much less for atomic hydrogen adsorbed on the surface. We also find that a single O or H atom on graphene has a higher energy than in the molecular state, while the adsorption of a single F atom is preferred over the gas phase. In addition, the energetics of graphane is reported. The calculated equilibrium lattice constant turns out to be larger than that of graphene, at variance with a recent experimental suggestion. PMID:22909778

  10. Quantum Monte Carlo simulations for disordered Bose systems

    SciTech Connect

    Trivedi, N.

    1992-03-01

    Interacting bosons in a random potential can be used to model {sup 3}He adsorbed in porous media, universal aspects of the superconductor-insulator transition in disordered films, and vortices in disordered type II superconductors. We study a model of bosons on a 2D square lattice with a random potential of strength V and on-site repulsion U. We first describe the path integral Monte Carlo algorithm used to simulate this system. The 2D quantum problem (at T=0) gets mapped onto a classical problem of strings or directed polymers moving in 3D with each string representing the world line of a boson. We discuss efficient ways of sampling the polymer configurations as well as the permutations between the bosons. We calculate the superfluid density and the excitation spectrum. Using these results we distinguish between a superfluid, a localized or Bose glass'' insulator with gapless excitations and a Mott insulator with a finite gap to excitations (found only at commensurate densities). We discover novel effects arising from the interpaly between V and U and present preliminary results for the phase diagram at incommensurate and commensurate densities.

  11. Quantum Monte Carlo simulations for disordered Bose systems

    SciTech Connect

    Trivedi, N.

    1992-03-01

    Interacting bosons in a random potential can be used to model {sup 3}He adsorbed in porous media, universal aspects of the superconductor-insulator transition in disordered films, and vortices in disordered type II superconductors. We study a model of bosons on a 2D square lattice with a random potential of strength V and on-site repulsion U. We first describe the path integral Monte Carlo algorithm used to simulate this system. The 2D quantum problem (at T=0) gets mapped onto a classical problem of strings or directed polymers moving in 3D with each string representing the world line of a boson. We discuss efficient ways of sampling the polymer configurations as well as the permutations between the bosons. We calculate the superfluid density and the excitation spectrum. Using these results we distinguish between a superfluid, a localized or ``Bose glass`` insulator with gapless excitations and a Mott insulator with a finite gap to excitations (found only at commensurate densities). We discover novel effects arising from the interpaly between V and U and present preliminary results for the phase diagram at incommensurate and commensurate densities.

  12. Cohesion Energetics of Carbon Allotropes: Quantum Monte Carlo Study

    SciTech Connect

    Shin, Hyeondeok; Kang, Sinabro; Koo, Jahyun; Lee, Hoonkyung; Kim, Jeongnim; Kwon, Yongkyung

    2014-01-01

    We have performed quantum Monte Carlo calculations to study the cohesion energetics of carbon allotropes, including sp3-bonded diamond, sp2-bonded graphene, sp-sp2 hybridized graphynes, and sp-bonded carbyne. The comput- ed cohesive energies of diamond and graphene are found to be in excellent agreement with the corresponding values de- termined experimentally for diamond and graphite, respectively, when the zero-point energies, along with the interlayer binding in the case of graphite, are included. We have also found that the cohesive energy of graphyne decreases system- atically as the ratio of sp-bonded carbon atoms increases. The cohesive energy of -graphyne, the most energetically- stable graphyne, turns out to be 6.766(6) eV/atom, which is smaller than that of graphene by 0.698(12) eV/atom. Experi- mental difficulty in synthesizing graphynes could be explained by their significantly smaller cohesive energies. Finally we conclude that the cohesive energy of a newly-proposed two-dimensional carbon network can be accurately estimated with the carbon-carbon bond energies determined from the cohesive energies of graphene and three different graphynes.

  13. Pseudopotentials for quantum Monte Carlo calculations of transition metal oxides

    NASA Astrophysics Data System (ADS)

    Krogel, Jaron; Santana, Juan; Kent, Paul; Reboredo, Fernando

    2015-03-01

    Quantum Monte Carlo calculations of transition metal oxides are partially limited by the availability of high quality pseudopotentials that are both accurate in QMC and compatible with major electronic structure codes, e.g. by not being overly hard in the standard planewave basis. Following insight gained from recent GW calculations, a set of neon core pseudopotentials with small cutoff radii have been created for the early transition metal elements Sc to Zn within the local density approximation of DFT. The pseudopotentials have been tested for energy consistency within QMC by calculating the first through fourth ionization potentials of the isolated transition metal (TM) atoms and the binding curve of each TM-O dimer. The vast majority of the ionization potentials fall within 0.3 eV of the experimental values, with exceptions occurring mainly for atoms with multiple unpaired d electrons where multireference effects are the strongest. The equilibrium bond lengths of the dimers are within 1% of experimental values and the binding energy errors are typically less than 0.3 eV. Given the uniform treatment of the core, the larger deviations occasionally observed may primarily reflect the limitations of a Slater-Jastrow trial wavefunction. This work is supported by the Materials Sciences & Engineering Division of the Office of Basic Energy Sciences, U.S. DOE. Research by PRCK was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

  14. Quantum Monte Carlo Simulation of condensed van der Waals Systems

    NASA Astrophysics Data System (ADS)

    Benali, Anouar; Shulenburger, Luke; Romero, Nichols A.; Kim, Jeongnim; Anatole von Lilienfeld, O.

    2012-02-01

    Van der Waals forces are as ubiquitous as infamous. While post-Hartree-Fock methods enable accurate estimates of these forces in molecules and clusters, they remain elusive for dealing with many-electron condensed phase systems. We present Quantum Monte Carlo [1,2] results for condensed van der Waals systems. Interatomic many-body contributions to cohesive energies and bulk modulus will be discussed. Numerical evidence is presented for crystals of rare gas atoms, and compared to experiments and methods [3]. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DoE's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.[4pt] [1] J. Kim, K. Esler, J. McMinis and D. Ceperley, SciDAC 2010, J. of Physics: Conference series, Chattanooga, Tennessee, July 11 2011 [0pt] [2] QMCPACK simulation suite, http://qmcpack.cmscc.org (unpublished)[0pt] [3] O. A. von Lillienfeld and A. Tkatchenko, J. Chem. Phys. 132 234109 (2010)

  15. Bond breaking with auxiliary-field quantum Monte Carlo.

    PubMed

    Al-Saidi, W A; Zhang, Shiwei; Krakauer, Henry

    2007-10-14

    Bond stretching mimics different levels of electron correlation and provides a challenging test bed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N(2) and in the H(50) chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N(2), we also study the use of multiple-determinant trial wave functions from multiconfiguration self-consistent-field calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit. PMID:17935380

  16. Quantum Monte Carlo for electronic structure: Recent developments and applications

    SciTech Connect

    Rodriquez, M. M.S.

    1995-04-01

    Quantum Monte Carlo (QMC) methods have been found to give excellent results when applied to chemical systems. The main goal of the present work is to use QMC to perform electronic structure calculations. In QMC, a Monte Carlo simulation is used to solve the Schroedinger equation, taking advantage of its analogy to a classical diffusion process with branching. In the present work the author focuses on how to extend the usefulness of QMC to more meaningful molecular systems. This study is aimed at questions concerning polyatomic and large atomic number systems. The accuracy of the solution obtained is determined by the accuracy of the trial wave function`s nodal structure. Efforts in the group have given great emphasis to finding optimized wave functions for the QMC calculations. Little work had been done by systematically looking at a family of systems to see how the best wave functions evolve with system size. In this work the author presents a study of trial wave functions for C, CH, C{sub 2}H and C{sub 2}H{sub 2}. The goal is to study how to build wave functions for larger systems by accumulating knowledge from the wave functions of its fragments as well as gaining some knowledge on the usefulness of multi-reference wave functions. In a MC calculation of a heavy atom, for reasonable time steps most moves for core electrons are rejected. For this reason true equilibration is rarely achieved. A method proposed by Batrouni and Reynolds modifies the way the simulation is performed without altering the final steady-state solution. It introduces an acceleration matrix chosen so that all coordinates (i.e., of core and valence electrons) propagate at comparable speeds. A study of the results obtained using their proposed matrix suggests that it may not be the optimum choice. In this work the author has found that the desired mixing of coordinates between core and valence electrons is not achieved when using this matrix. A bibliography of 175 references is included.

  17. Quantum Monte Carlo calculations for point defects in semiconductors

    NASA Astrophysics Data System (ADS)

    Hennig, Richard

    2010-03-01

    Point defects in silicon have been studied extensively for many years. Nevertheless the mechanism for self diffusion in Si is still debated. Direct experimental measurements of the selfdiffusion in silicon are complicated by the lack of suitable isotopes. Formation energies are either obtained from theory or indirectly through the analysis of dopant and metal diffusion experiments. Density functional calculations predict formation energies ranging from 3 to 5 eV depending on the approximations used for the exchange-correlation functional [1]. Analysis of dopant and metal diffusion experiments result in similar broad range of diffusion activation energies of 4.95 [2], 4.68 [3], 2.4 eV [4]. Assuming a migration energy barrier of 0.1-0.3 eV [5], the resulting experimental interstitial formation energies range from 2.1 - 4.9 eV. To answer the question of the formation energy of Si interstitials we resort to a many-body description of the wave functions using quantum Monte Carlo (QMC) techniques. Previous QMC calculations resulted in formation energies for the interstitials of around 5 eV [1,6]. We present a careful analysis of all the controlled and uncontrolled approximations that affect the defect formation energies in variational and diffusion Monte Carlo calculations. We find that more accurate trial wave functions for QMC using improved Jastrow expansions and most importantly a backflow transformation for the electron coordinates significantly improve the wave functions. Using zero-variance extrapolation, we predict interstitial formation energies in good agreement with hybrid DFT functionals [1] and recent GW calculations [7]. [4pt] [1] E. R. Batista, J. Heyd, R. G. Hennig, B. P. Uberuaga, R. L. Martin, G. E. Scuseria, C. J. Umrigar, and J. W. Wilkins. Phys. Rev. B 74, 121102(R) (2006).[0pt] [2] H. Bracht, E. E. Haller, and R. Clark-Phelps, Phys. Rev. Lett. 81, 393 (1998). [0pt] [3] A. Ural, P. B. Griffin, and J. D. Plummer, Phys. Rev. Lett. 83, 3454 (1999). [0pt

  18. Quantum Monte Carlo methods and lithium cluster properties

    SciTech Connect

    Owen, R.K.

    1990-12-01

    Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) [0.1981], 0.1895(9) [0.1874(4)], 0.1530(34) [0.1599(73)], 0.1664(37) [0.1724(110)], 0.1613(43) [0.1675(110)] Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) [0.0203(12)], 0.0188(10) [0.0220(21)], 0.0247(8) [0.0310(12)], 0.0253(8) [0.0351(8)] Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.

  19. Quantum Monte Carlo methods and lithium cluster properties. [Atomic clusters

    SciTech Connect

    Owen, R.K.

    1990-12-01

    Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) (0.1981), 0.1895(9) (0.1874(4)), 0.1530(34) (0.1599(73)), 0.1664(37) (0.1724(110)), 0.1613(43) (0.1675(110)) Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) (0.0203(12)), 0.0188(10) (0.0220(21)), 0.0247(8) (0.0310(12)), 0.0253(8) (0.0351(8)) Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.

  20. Excited states of methylene from quantum Monte Carlo.

    PubMed

    Zimmerman, Paul M; Toulouse, Julien; Zhang, Zhiyong; Musgrave, Charles B; Umrigar, C J

    2009-09-28

    The ground and lowest three adiabatic excited states of methylene are computed using the variational Monte Carlo and diffusion Monte Carlo (DMC) methods using progressively larger Jastrow-Slater multideterminant complete active space (CAS) wave functions. The highest of these states has the same symmetry, (1)A(1), as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment, but single-determinant wave functions do not yield accurate DMC energies of the states of (1)A(1) symmetry, indicating that it is important to include in the wave function Slater determinants that describe static (strong) correlation. Excitation energies obtained using recently proposed pseudopotentials [Burkatzki et al., J. Chem. Phys. 126, 234105 (2007)] differ from the all-electron excitation energies by at most 0.04 eV. PMID:19791848

  1. Variational quantum Monte Carlo ground state of lithium on a Slater orbital basis

    NASA Astrophysics Data System (ADS)

    Eckstein, H.; Schattke, W.

    1995-02-01

    The ground state of bulk lithium at zero temperature is simulated by the variational quantum Monte Carlo algorithm. The total energy and its constituents are determined for two parametrized sets of trial wave functions. Including correlation by a Jastrow factor the one-determinant ansatz consists of either plane waves or a linear combination of Slater orbitals for the Li 2 s states. The latter yields results near those of the diffusion Monte Carlo algorithm.

  2. Communication: Variation after response in quantum Monte Carlo.

    PubMed

    Neuscamman, Eric

    2016-08-28

    We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster's accuracy for excitations with significant doubly excited character. PMID:27586897

  3. Quantum Monte Carlo Methods for First Principles Simulation of Liquid Water

    ERIC Educational Resources Information Center

    Gergely, John Robert

    2009-01-01

    Obtaining an accurate microscopic description of water structure and dynamics is of great interest to molecular biology researchers and in the physics and quantum chemistry simulation communities. This dissertation describes efforts to apply quantum Monte Carlo methods to this problem with the goal of making progress toward a fully "ab initio"…

  4. Polynomial-time-scaling quantum dynamics with time-dependent quantum Monte Carlo.

    PubMed

    Christov, Ivan P

    2009-05-21

    Here we study the dynamics of many-body quantum systems using the time-dependent quantum Monte Carlo method where the evolution is described by ensembles of particles and guide waves. The exponential time scaling inherent to the quantum many-body problem is reduced to polynomial-time computation by solving concurrently a set of coupled Schrodinger equations for the guide waves in physical space and a set of first-order equations for the Monte Carlo walkers. We use effective potentials to account for the local and nonlocal quantum correlations in time-varying fields, where for fermionic states an exchange "hole" is introduced explicitly through screened Coulomb potentials. The walker distributions for the ground states of para- and ortho-helium reproduce well the statistical properties, such as the electron-pair density function, of the real atoms. Our predictions for the dipole response and the ionization of an atom exposed to strong ultrashort optical pulse are in good agreement with the exact results. PMID:19391581

  5. Quantum Monte Carlo simulation of spin-polarized H

    SciTech Connect

    Markic, L. Vranjes; Boronat, J.; Casulleras, J.

    2007-02-01

    The ground-state properties of spin polarized hydrogen H{down_arrow} are obtained by means of diffusion Monte Carlo calculations. Using the most accurate to date ab initio H{down_arrow}-H{down_arrow} interatomic potential we have studied its gas phase, from the very dilute regime until densities above its freezing point. At very small densities, the equation of state of the gas is very well described in terms of the gas parameter {rho}a{sup 3}, with a the s-wave scattering length. The solid phase has also been studied up to high pressures. The gas-solid phase transition occurs at a pressure of 173 bar, a much higher value than suggested by previous approximate descriptions.

  6. Quantum Monte Carlo calculations of neutron and nuclear matter

    NASA Astrophysics Data System (ADS)

    Gandolfi, Stefano

    2014-09-01

    Recent advances in experiments of the symmetry energy of nuclear matter and in neutron star observations yield important new insights on the equation of state of neutron matter at nuclear densities. In this regime the EOS of neutron matter plays a critical role in determining the mass-radius relationship for neutron stars. We show how microscopic calculations of neutron matter, based on realistic two- and three-nucleon forces, make clear predictions for the relation between the isospin-asymmetry energy of nuclear matter and its density dependence, and the maximum mass and radius for a neutron star. We will also discuss the recent extension of the Auxiliary Field Diffusion Monte Carlo method to study the equation of state of nuclear matter using two-body nucleon interactions. The equation of state of isospin-asymmetric nuclear matter will also be discussed.

  7. Quantum Monte Carlo calculation of the properties of atomic carbon and diamond

    SciTech Connect

    Fahy, S.; Wang, X.W.; Louie, S.G.

    1988-06-01

    A new method of calculating total energies of solids using non-local pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented. By using pseudopotentials, the large fluctuations of the energies in the core region of the atoms which occur in quantum Monte Carlo all-electron schemes are avoided. The method is applied to calculate the cohesive energy and structural properties of diamond and the first ionization energy and electron affinity of the carbon atom. Results are in excellent agreement with experiment. 8 refs., 1 fig., 2 tabs.

  8. Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems

    SciTech Connect

    Azadi, Sam Foulkes, W. M. C.

    2015-09-14

    We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.

  9. Spin-orbit interactions in electronic structure quantum Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Melton, Cody A.; Zhu, Minyi; Guo, Shi; Ambrosetti, Alberto; Pederiva, Francesco; Mitas, Lubos

    2016-04-01

    We develop generalization of the fixed-phase diffusion Monte Carlo method for Hamiltonians which explicitly depends on particle spins such as for spin-orbit interactions. The method is formulated in a zero-variance manner and is similar to the treatment of nonlocal operators in commonly used static-spin calculations. Tests on atomic and molecular systems show that it is very accurate, on par with the fixed-node method. This opens electronic structure quantum Monte Carlo methods to a vast research area of quantum phenomena in which spin-related interactions play an important role.

  10. i QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit

    NASA Astrophysics Data System (ADS)

    Huang, Li; Wang, Yilin; Meng, Zi Yang; Du, Liang; Werner, Philipp; Dai, Xi

    2015-10-01

    Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed i QIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for i QIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of i QIST.

  11. Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study

    SciTech Connect

    Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A

    2014-01-01

    We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.

  12. Path-integral Monte Carlo study of asymmetric quantum quadrupolar rotors with fourth-order propagators

    NASA Astrophysics Data System (ADS)

    Park, Sungjin; Shin, Hyeondeok; Kwon, Yongkyung

    2012-08-01

    The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.

  13. An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism

    NASA Astrophysics Data System (ADS)

    Sellier, J. M.; Nedjalkov, M.; Dimov, I.

    2015-05-01

    The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consists of three main parts. First, we introduce the Wigner formalism, then we discuss in detail the Wigner Monte Carlo method and, finally, we present practical applications. In particular, the Wigner model is first derived from the Schrödinger equation. Then a generalization of the formalism due to Moyal is provided, which allows to recover important mathematical properties of the model. Next, the Wigner equation is further generalized to the case of many-body quantum systems. Finally, a physical interpretation of the negative part of a quasi-distribution function is suggested. In the second part, the Wigner Monte Carlo method, based on the concept of signed (virtual) particles, is introduced in detail for the single-body problem. Two extensions of the Wigner Monte Carlo method to quantum many-body problems are introduced, in the frameworks of time-dependent density functional theory and ab-initio methods. Finally, in the third and last part of this paper, applications to single- and many-body problems are performed in the context of quantum physics and quantum chemistry, specifically focusing on the hydrogen, lithium and boron atoms, the H2 molecule and a system of two identical Fermions. We conclude this work with a discussion on the still unexplored directions the Wigner Monte Carlo method could take in the next future.

  14. Quantum Monte Carlo studies of relativistic effects in light nuclei

    SciTech Connect

    J. L. Forest; V. R. Pandharipande; A. Arriaga

    1998-05-01

    Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work the authors use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of {sup 3}H and {sup 4}He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in {sup 3}H ({sup 4}He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.

  15. Hyperon Puzzle: Hints from Quantum Monte Carlo Calculations

    NASA Astrophysics Data System (ADS)

    Lonardoni, Diego; Lovato, Alessandro; Gandolfi, Stefano; Pederiva, Francesco

    2015-03-01

    The onset of hyperons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions and recent astrophysical observations of neutron stars are the grounds for the so-called hyperon puzzle. We calculate the equation of state and the neutron star mass-radius relation of an infinite systems of neutrons and Λ particles by using the auxiliary field diffusion Monte Carlo algorithm. We find that the three-body hyperon-nucleon interaction plays a fundamental role in the softening of the equation of state and for the consequent reduction of the predicted maximum mass. We have considered two different models of three-body force that successfully describe the binding energy of medium mass hypernuclei. Our results indicate that they give dramatically different results on the maximum mass of neutron stars, not necessarily incompatible with the recent observation of very massive neutron stars. We conclude that stronger constraints on the hyperon-neutron force are necessary in order to properly assess the role of hyperons in neutron stars.

  16. Hyperon puzzle: hints from quantum Monte Carlo calculations.

    PubMed

    Lonardoni, Diego; Lovato, Alessandro; Gandolfi, Stefano; Pederiva, Francesco

    2015-03-01

    The onset of hyperons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions and recent astrophysical observations of neutron stars are the grounds for the so-called hyperon puzzle. We calculate the equation of state and the neutron star mass-radius relation of an infinite systems of neutrons and Λ particles by using the auxiliary field diffusion Monte Carlo algorithm. We find that the three-body hyperon-nucleon interaction plays a fundamental role in the softening of the equation of state and for the consequent reduction of the predicted maximum mass. We have considered two different models of three-body force that successfully describe the binding energy of medium mass hypernuclei. Our results indicate that they give dramatically different results on the maximum mass of neutron stars, not necessarily incompatible with the recent observation of very massive neutron stars. We conclude that stronger constraints on the hyperon-neutron force are necessary in order to properly assess the role of hyperons in neutron stars. PMID:25793808

  17. Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Christov, Ivan P.

    2016-08-01

    In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.

  18. Monte Carlo Benchmark

    2010-10-20

    The "Monte Carlo Benchmark" (MCB) is intended to model the computatiional performance of Monte Carlo algorithms on parallel architectures. It models the solution of a simple heuristic transport equation using a Monte Carlo technique. The MCB employs typical features of Monte Carlo algorithms such as particle creation, particle tracking, tallying particle information, and particle destruction. Particles are also traded among processors using MPI calls.

  19. Quantum Monte Carlo Simulations of Adulteration Effect on Bond Alternating Spin=1/2 Chain

    NASA Astrophysics Data System (ADS)

    Zhang, Peng; Xu, Zhaoxin; Ying, Heping; Dai, Jianhui; Crompton, Peter

    The S=1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.

  20. Quantum-trajectory Monte Carlo method for study of electron-crystal interaction in STEM.

    PubMed

    Ruan, Z; Zeng, R G; Ming, Y; Zhang, M; Da, B; Mao, S F; Ding, Z J

    2015-07-21

    In this paper, a novel quantum-trajectory Monte Carlo simulation method is developed to study electron beam interaction with a crystalline solid for application to electron microscopy and spectroscopy. The method combines the Bohmian quantum trajectory method, which treats electron elastic scattering and diffraction in a crystal, with a Monte Carlo sampling of electron inelastic scattering events along quantum trajectory paths. We study in this work the electron scattering and secondary electron generation process in crystals for a focused incident electron beam, leading to understanding of the imaging mechanism behind the atomic resolution secondary electron image that has been recently achieved in experiment with a scanning transmission electron microscope. According to this method, the Bohmian quantum trajectories have been calculated at first through a wave function obtained via a numerical solution of the time-dependent Schrödinger equation with a multislice method. The impact parameter-dependent inner-shell excitation cross section then enables the Monte Carlo sampling of ionization events produced by incident electron trajectories travelling along atom columns for excitation of high energy knock-on secondary electrons. Following cascade production, transportation and emission processes of true secondary electrons of very low energies are traced by a conventional Monte Carlo simulation method to present image signals. Comparison of the simulated image for a Si(110) crystal with the experimental image indicates that the dominant mechanism of atomic resolution of secondary electron image is the inner-shell ionization events generated by a high-energy electron beam. PMID:26082190

  1. Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data

    SciTech Connect

    Gubernatis, J.E.; Bonca, J.; Jarrell, M.

    1995-12-31

    We present brief description of how methods of Bayesian inference are used to obtain real frequency information by the analytic continuation of imaginary-time quantum Monte Carlo data. We present the procedure we used, which is due to R. K. Bryan, and summarize several bottleneck issues.

  2. Monte-Carlo Quantum Chemistry of Biogene Amines. Laser and Neutron Capture Effects

    SciTech Connect

    Glushkov, A. V.; Malinovskaya, S. V.; Khetselius, O. Yu.; Loboda, A. V.

    2009-03-09

    Monte-Carlo quantum calculation of the cluster consisting of the serotonine ST (histamine HM) molecules and 100 molecules of water is carried out. It is found that the zwitterion appears as expected to be strongly favoured with respect to neutral molecule. The perspective possibilities of laser and neutron capture action on different biomolecules are indicated.

  3. Monte-Carlo Quantum Chemistry of Biogene Amines. Laser and Neutron Capture Effects

    NASA Astrophysics Data System (ADS)

    Glushkov, A. V.; Malinovskaya, S. V.; Khetselius, O. Yu.; Loboda, A. V.

    2009-03-01

    Monte-Carlo quantum calculation of the cluster consisting of the serotonine ST (histamine HM) molecules and 100 molecules of water is carried out. It is found that the zwitterion appears as expected to be strongly favoured with respect to neutral molecule. The perspective possibilities of laser and neutron capture action on different biomolecules are indicated.

  4. Grover search algorithm with Rydberg-blockaded atoms: quantum Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Petrosyan, David; Saffman, Mark; Mølmer, Klaus

    2016-05-01

    We consider the Grover search algorithm implementation for a quantum register of size N={2}k using k (or k+1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by Mølmer et al (2011 J. Phys. B 44 184016). We suggest some simplifications for the microwave and laser couplings, and analyze the performance of the algorithm for up to k = 4 multilevel atoms under realistic experimental conditions using quantum stochastic (Monte Carlo) wavefunction simulations.

  5. Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations

    NASA Astrophysics Data System (ADS)

    Huang, Chien-Jung; Umrigar, C. J.; Nightingale, M. P.

    1997-08-01

    Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based on the theory of invariants is used to compute the high-body correlations. We observe significant improvements in the variational Monte Carlo energy and in the fluctuations of the local energies but not in the fixed-node diffusion Monte Carlo energies. Improvements for the ground states of physical, fermionic atoms are found to be smaller than those for the ground states of fictitious, bosonic atoms, indicating that errors in the nodal surfaces of the fermionic wave functions are a limiting factor.

  6. Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study.

    PubMed

    Beaudet, Todd D; Casula, Michele; Kim, Jeongnim; Sorella, Sandro; Martin, Richard M

    2008-10-28

    We present a quantum Monte Carlo study of the hydrogen-benzene system where binding is very weak. We demonstrate that the binding is well described at both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels by a Jastrow correlated single determinant geminal wave function with an optimized compact basis set that includes diffuse orbitals. Agreement between VMC and fixed-node DMC binding energies is found to be within 0.18 mhartree, suggesting that the calculations are well converged with respect to the basis. Essentially the same binding is also found in independent DMC calculations using a different trial wave function of a more conventional Slater-Jastrow form, supporting our conclusion that the binding energy is accurate and includes all effects of correlation. We compare with previous calculations, and we discuss the physical mechanisms of the interaction, the role of diffuse basis functions, and the charge redistribution in the bond. PMID:19045302

  7. Reaching the ground state of a quantum spin glass using a zero-temperature quantum Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Das, Arnab; Chakrabarti, Bikas K.

    2008-12-01

    Here we discuss the annealing behavior of an infinite-range ±J Ising spin glass in the presence of a transverse field using a zero-temperature quantum Monte Carlo method. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particular, when the transverse field is low, much more efficiently.

  8. Reaching the ground state of a quantum spin glass using a zero-temperature quantum Monte Carlo method.

    PubMed

    Das, Arnab; Chakrabarti, Bikas K

    2008-12-01

    Here we discuss the annealing behavior of an infinite-range +/-J Ising spin glass in the presence of a transverse field using a zero-temperature quantum Monte Carlo method. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particular, when the transverse field is low, much more efficiently. PMID:19256816

  9. Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Maik, Michał; Hauke, Philipp; Dutta, Omjyoti; Zakrzewski, Jakub; Lewenstein, Maciej

    2012-11-01

    We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U(1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density-density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.

  10. Quantum Monte Carlo Studies of Interaction-Induced Localization in Quantum Dots and Wires

    NASA Astrophysics Data System (ADS)

    Devrim Güçlü, A.

    2009-03-01

    We investigate interaction-induced localization of electrons in both quantum dots and inhomogeneous quantum wires using variational and diffusion quantum Monte Carlo methods. Quantum dots and wires are highly tunable systems that enable the study of the physics of strongly correlated electrons. With decreasing electronic density, interactions become stronger and electrons are expected to localize at their classical positions, as in Wigner crystallization in an infinite 2D system. (1) Dots: We show that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over is, then, a signature of localization; it occurs near rs˜20. For higher values of rs, the configuration symmetry of the quantum dot becomes fully consistent with the classical ground state. (2) Wires: We study an inhomogeneous quasi-one-dimensional system -- a wire with two regions, one at low density and the other high. We find that strong localization occurs in the low density quantum point contact region as the gate potential is increased. The nature of the transition from high to low density depends on the density gradient -- if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. We find no evidence for ferromagnetic spin polarization for the range of parameters studied. The picture emerging here is in good agreement with the experimental measurements of tunneling between two wires. Collaborators: C. J. Umrigar (Cornell), Hong Jiang (Fritz Haber Institut), Amit Ghosal (IISER Calcutta), and H. U. Baranger (Duke).

  11. Bohm trajectories for the Monte Carlo simulation of quantum-based devices

    NASA Astrophysics Data System (ADS)

    Oriols, X.; García-García, J. J.; Martín, F.; Suñé, J.; González, T.; Mateos, J.; Pardo, D.

    1998-02-01

    A generalization of the classical ensemble Monte Carlo (MC) device simulation technique is proposed to simultaneously deal with quantum-mechanical phase-coherence effects and scattering interactions in quantum-based devices. The proposed method restricts the quantum treatment of transport to the regions of the device where the potential profile significantly changes in distances of the order of the de Broglie wavelength of the carriers (the quantum window). Bohm trajectories associated to time-dependent Gaussian wave packets are used to simulate the electron transport in the quantum window. Outside this window, the classical ensemble MC simulation technique is used. Classical and quantum trajectories are smoothly matched at the boundaries of the quantum window according to a criterium of total-energy conservation. A self-consistent one-dimensional simulator for resonant tunneling diodes has been developed to demonstrate the feasibility of our proposal.

  12. Monte Carlo Example Programs

    2006-05-09

    The Monte Carlo example programs VARHATOM and DMCATOM are two small, simple FORTRAN programs that illustrate the use of the Monte Carlo Mathematical technique for calculating the ground state energy of the hydrogen atom.

  13. Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Azadi, Sam; Cohen, R. E.

    2016-08-01

    We studied the low-pressure (0-10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P21/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P21/c phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.

  14. Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations

    NASA Astrophysics Data System (ADS)

    Wei, Z. C.; Wu, Congjun; Li, Yi; Zhang, Shiwei; Xiang, T.

    2016-06-01

    The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry, and interacting topological insulators with spin-flip terms.

  15. Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations.

    PubMed

    Wei, Z C; Wu, Congjun; Li, Yi; Zhang, Shiwei; Xiang, T

    2016-06-24

    The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry, and interacting topological insulators with spin-flip terms. PMID:27391709

  16. Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Tokár, K.; Derian, R.; Mitas, L.; Štich, I.

    2016-02-01

    Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances.

  17. Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo

    SciTech Connect

    Overy, Catherine; Blunt, N. S.; Shepherd, James J.; Booth, George H.; Cleland, Deidre; Alavi, Ali

    2014-12-28

    Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

  18. Charged vanadium-benzene multidecker clusters: DFT and quantum Monte Carlo study.

    PubMed

    Tokár, K; Derian, R; Mitas, L; Štich, I

    2016-02-14

    Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo provides an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances. PMID:26874484

  19. Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study

    NASA Astrophysics Data System (ADS)

    Pilati, Sebastiano; Zintchenko, Ilia; Troyer, Matthias

    2015-05-01

    We investigate the ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of a periodic potential that describes the effect of a 3D optical lattice, using continuous-space quantum Monte Carlo simulations. We find that a shallow optical lattice below half-filling strongly favors the ferromagnetic instability compared to the homogeneous Fermi gas. Instead, in the regime of deep optical lattices and weak interactions, where the conventional description in terms of single-band tight-binding models is reliable, our results indicate that the paramagnetic state is stable, in agreement with previous quantum Monte Carlo simulations of the Hubbard model. Our findings shed light on the important role played by multi-band effects and by interaction-induced hopping in the physics of atomic gases trapped in optical lattices.

  20. Communication: Fixed-node errors in quantum Monte Carlo: Interplay of electron density and node nonlinearities

    SciTech Connect

    Rasch, Kevin M.; Hu, Shuming; Mitas, Lubos

    2014-01-28

    We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference in the valence fixed-node biases is studied across a set of atoms, molecules, and also Si, C solid crystals. We show that the key features which affect the fixed-node errors are the differences in electron density and the degree of node nonlinearity. The findings reveal how the accuracy of the quantum Monte Carlo varies across a variety of systems, provide new perspectives on the origins of the fixed-node biases in calculations of molecular and condensed systems, and carry implications for pseudopotential constructions for heavy elements.

  1. A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo.

    PubMed

    Aspuru-Guzik, Alán; Salomón-Ferrer, Romelia; Austin, Brian; Lester, William A

    2005-05-01

    A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size. PMID:15761862

  2. Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States.

    PubMed

    Guareschi, Riccardo; Zulfikri, Habiburrahman; Daday, Csaba; Floris, Franca Maria; Amovilli, Claudio; Mennucci, Benedetta; Filippi, Claudia

    2016-04-12

    We present for the first time a quantum mechanics/molecular mechanics scheme which combines quantum Monte Carlo with the reaction field of classical polarizable dipoles (QMC/MMpol). In our approach, the optimal dipoles are self-consistently generated at the variational Monte Carlo level and then used to include environmental effects in diffusion Monte Carlo. We investigate the performance of this hybrid model in describing the vertical excitation energies of prototypical small molecules solvated in water, namely, methylenecyclopropene and s-trans acrolein. Two polarization regimes are explored where either the dipoles are optimized with respect to the ground-state solute density (polGS) or different sets of dipoles are separately brought to equilibrium with the states involved in the electronic transition (polSS). By comparing with reference supermolecular calculations where both solute and solvent are treated quantum mechanically, we find that the inclusion of the response of the environment to the excitation of the solute leads to superior results than the use of a frozen environment (point charges or polGS), in particular, when the solute-solvent coupling is dominated by electrostatic effects which are well recovered in the polSS condition. QMC/MMpol represents therefore a robust scheme to treat important environmental effects beyond static point charges, combining the accuracy of QMC with the simplicity of a classical approach. PMID:26959751

  3. Structural Optimization by Quantum Monte Carlo: Investigating the Low-Lying Excited States of Ethylene

    PubMed Central

    Barborini, Matteo; Sorella, Sandro; Guidoni, Leonardo

    2014-01-01

    We present full structural optimizations of the ground state and of the low lying triplet state of the ethylene molecule by means of Quantum Monte Carlo methods. Using the efficient structural optimization method based on renormalization techniques and on adjoint differentiation algorithms recently proposed [Sorella, S.; Capriotti, L. J. Chem. Phys. 2010, 133, 234111], we present the variational convergence of both wave function parameters and atomic positions. All of the calculations were done using an accurate and compact wave function based on Pauling’s resonating valence bond representation: the Jastrow Antisymmetrized Geminal Power (JAGP). All structural and wave function parameters are optimized, including coefficients and exponents of the Gaussian primitives of the AGP and the Jastrow atomic orbitals. Bond lengths and bond angles are calculated with a statistical error of about 0.1% and are in good agreement with the available experimental data. The Variational and Diffusion Monte Carlo calculations estimate vertical and adiabatic excitation energies in the ranges 4.623(10)–4.688(5) eV and 3.001(5)–3.091(5) eV, respectively. The adiabatic gap, which is in line with other correlated quantum chemistry methods, is slightly higher than the value estimated by recent photodissociation experiments. Our results demonstrate how Quantum Monte Carlo calculations have become a promising and computationally affordable tool for the structural optimization of correlated molecular systems. PMID:24634617

  4. The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

    NASA Astrophysics Data System (ADS)

    Lu, Shih-I.

    2004-12-01

    For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.

  5. Quantum Monte Carlo simulation of resonant tunneling diodes based on the Wigner distribution function formalism

    NASA Astrophysics Data System (ADS)

    García-García, J.; Martín, F.; Oriols, X.; Suñé, J.

    1998-12-01

    A tool for the simulation of resonant tunneling diodes (RTDs) has been developed. This is based on the solution of the quantum Liouville equation in the active region of the device and the Boltzman transport equation in the regions adjacent to the contacts by means of a Monte Carlo algorithm. By accurately coupling both approaches to current transport, we have developed a quantum simulation tool that allows the use of simulation domains much larger and realistic than those previously considered, without a significant increase in computational burden. The main characteristics expected for the considered devices are clearly obtained, thus supporting the validity of our tool for the simulation of RTDs.

  6. Ab initio quantum Monte Carlo calculations of ground-state properties of manganese's oxides

    NASA Astrophysics Data System (ADS)

    Sharma, Vinit; Krogel, Jaron T.; Kent, P. R. C.; Reboredo, Fernando A.

    One of the critical scientific challenges of contemporary research is to obtain an accurate theoretical description of the electronic properties of strongly correlated systems such as transition metal oxides and rare-earth compounds, since state-of-art ab-initio methods based on approximate density functionals are not always sufficiently accurate. Quantum Monte Carlo (QMC) methods, which use statistical sampling to evaluate many-body wave functions, have the potential to answer this challenge. Owing to the few fundamental approximations made and the direct treatment of electron correlation, QMC methods are among the most accurate electronic structure methods available to date. We assess the accuracy of the diffusion Monte Carlo method in the case of rocksalt manganese oxide (MnO). We study the electronic properties of this strongly-correlated oxide, which has been identified as a suitable candidate for many applications ranging from catalysts to electronic devices. ``This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.'' Ab initio quantum Monte Carlo calculations of ground-state properties of manganese's oxides.

  7. Quantum Monte Carlo calculations of excited states in A=6-8 nuclei

    SciTech Connect

    Pieper, Steven C.; Wiringa, R.B.; Carlson, J.

    2004-11-01

    A variational Monte Carlo method is used to generate sets of orthogonal trial functions, {psi}{sub T}(J{sup {pi}};T), for given quantum numbers in various light p-shell nuclei. These {psi}{sub T} are then used as input to Green's function Monte Carlo (GFMC) calculations of first, second, and higher excited (J{sup {pi}};T) states. Realistic two- and three-nucleon interactions are used. We find that if the physical excited state is reasonably narrow, the GFMC energy converges to a stable result. With the combined Argonne v{sub 18} two-nucleon and Illinois-2 three-nucleon interactions, the results for many second and higher states in A=6-8 nuclei are close to the experimental values.

  8. Electron density of states of Fe-based superconductors: Quantum trajectory Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Kashurnikov, V. A.; Krasavin, A. V.; Zhumagulov, Ya. V.

    2016-03-01

    The spectral and total electron densities of states in two-dimensional FeAs clusters, which simulate iron-based superconductors, have been calculated using the generalized quantum Monte Carlo algorithm within the full two-orbital model. Spectra have been reconstructed by solving the integral equation relating the Matsubara Green's function and spectral density by the method combining the gradient descent and Monte Carlo algorithms. The calculations have been performed for clusters with dimensions up to 10 × 10 FeAs cells. The profiles of the Fermi surface for the entire Brillouin zone have been presented in the quasiparticle approximation. Data for the total density of states near the Fermi level have been obtained. The effect of the interaction parameter, size of the cluster, and temperature on the spectrum of excitations has been studied.

  9. Quantum Monte Carlo calculations of neutron matter with chiral three-body forces

    NASA Astrophysics Data System (ADS)

    Tews, I.; Gandolfi, S.; Gezerlis, A.; Schwenk, A.

    2016-02-01

    Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N2LO ). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. In particular, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.

  10. Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms

    NASA Astrophysics Data System (ADS)

    Lin, C.; Zong, F. H.; Ceperley, D. M.

    2001-07-01

    We develop and test Quantum Monte Carlo algorithms that use a``twist'' or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy and has the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.

  11. Quantum Monte Carlo studies of Shannon-Renyi entropies and participation spectra in interacting spin systems

    NASA Astrophysics Data System (ADS)

    Luitz, David J.; Alet, Fabien; Laflorencie, Nicolas

    2014-03-01

    Shannon-Renyi entropies are measures of the participation of basis states in a wave function. Previous work for one dimensional systems showed that they exhibit a subleading scaling behavior with system size that contains universal information, such as e.g. the Luttinger Liquid parameter. Here, we introduce quantum Monte Carlo schemes to calculate these quantities and the related participation spectra for unfrustrated quantum many body systems in any dimension and apply them to interacting spin systems. Our results demonstrate the universality of subleading scaling terms for different kinds of phase transitions with a spontaneous breaking of discrete or continuous symmetries and at quantum critical points. Aditionally, we also discuss the signature of quantum phase transitions in the participation spectra of subsystems.

  12. Quantum Monte Carlo algorithms for electronic structure at the petascale; the endstation project.

    SciTech Connect

    Kim, J; Ceperley, D M; Purwanto, W; Walter, E J; Krakauer, H; Zhang, S W; Kent, P.R. C; Hennig, R G; Umrigar, C; Bajdich, M; Kolorenc, J; Mitas, L; Srinivasan, A

    2008-10-01

    Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrodinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.

  13. Monte Carlo fundamentals

    SciTech Connect

    Brown, F.B.; Sutton, T.M.

    1996-02-01

    This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.

  14. Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions

    NASA Astrophysics Data System (ADS)

    Wang, Lei; Iazzi, Mauro; Corboz, Philippe; Troyer, Matthias

    2015-06-01

    We present the ground state extension of the efficient continuous-time quantum Monte Carlo algorithm for lattice fermions of M. Iazzi and M. Troyer, Phys. Rev. B 91, 241118 (2015), 10.1103/PhysRevB.91.241118. Based on continuous-time expansion of an imaginary-time projection operator, the algorithm is free of systematic error and scales linearly with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless t -V model as an example and compare the numerical results with exact diagonalization, density matrix renormalization group, and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.

  15. Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

    NASA Astrophysics Data System (ADS)

    Suwa, Hidemaro

    2013-03-01

    We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad

  16. Quantum Monte-Carlo simulation of spin-one antiferromagnets with single-ion anisotropy

    NASA Astrophysics Data System (ADS)

    Kato, Yasuyuki; Wierschem, Keola; Nishida, Yusuke; Batista, Cristian; Sengupta, Pinaki

    2013-03-01

    We study a spin-one Heisenberg model with uniaxial single-ion anisotropy, D, and Zeeman coupling to a magnetic field, B, parallel to the symmetry axis. We compute the (D / J , B / J) quantum phase diagram for square and simple cubic lattices by combining analytical and Quantum Monte Carlo approaches, and find a transition between XY-antiferromagnetic and ferronematic phases that spontaneously break the U(1) symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. For the efficient simulation of ferronematic phase, we developed and implemented a new multi-discontinuity algorithm based on the directed-loop algorithm. The ordinary quantum Monte-Carlo methods fall into freezing problems when we apply them to this system at large D / J and finite B / J ~ 1 . The new method does not suffer from the freezing problems. This research used resources of the NERSCC (DOE Contract No. DE-AC02-05CH11231). Work at LANL was performed under the auspices of a J. Robert Oppenheimer Fellowship and the U.S. DOE contract No. DE-AC52-06NA25396 through the LDRD program.

  17. A Monte Carlo-quantum mechanics study of a solvatochromic π* probe.

    PubMed

    Domínguez, Moisés; Rezende, Marcos Caroli

    2016-09-01

    The solvation and the solvatochromic behavior of 5-(dimethylamino)-5'-nitro-2,2'-bithiophene 1, the basis of a π* scale of solvent polarities, was investigated theoretically in toluene, dichloromethane, methanol and formamide with a Monte Carlo and quantum mechanics (QM/MM) iterative approach. The calculated transition energies of the solvatochromic band of 1, obtained as averages of statistically uncorrelated configurations, including the solute and explicit solvent molecules of the first solvation layer, besides showing good agreement with the experimental transitions, reproduced very well the positive solvatochromism of this probe in various solvents. PMID:27553303

  18. Neutron matter with Quantum Monte Carlo: chiral 3N forces and static response

    NASA Astrophysics Data System (ADS)

    Buraczynski, M.; Gandolfi, S.; Gezerlis, A.; Schwenk, A.; Tews, I.

    2016-03-01

    Neutron matter is related to the physics of neutron stars and that of neutron-rich nuclei. Quantum Monte Carlo (QMC) methods offer a unique way of solving the many-body problem non-perturbatively, providing feedback on features of nuclear interactions and addressing scenarios that are inaccessible to other approaches. In this contribution we go over two recent accomplishments in the theory of neutron matter: a) the fusing of QMC with chiral effective field theory interactions, focusing on local chiral 3N forces, and b) the first attempt to find an ab initio solution to the problem of static response.

  19. Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

    NASA Astrophysics Data System (ADS)

    Calcavecchia, Francesco; Holzmann, Markus

    2016-04-01

    We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.

  20. Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction.

    PubMed

    Calcavecchia, Francesco; Holzmann, Markus

    2016-04-01

    We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity. PMID:27176442

  1. Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

    2014-10-01

    We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing density functional theory (DFT) and quantum Monte Carlo (QMC) treatments. The method is applied to address the longstanding discrepancy between DFT calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, in contrast to DAC data.

  2. Neutron matter with Quantum Monte Carlo: chiral 3N forces and static response

    DOE PAGESBeta

    Buraczynski, M.; Gandolfi, S.; Gezerlis, A.; Schwenk, A.; Tews, I.

    2016-03-01

    Neutron matter is related to the physics of neutron stars and that of neutron-rich nuclei. Moreover, Quantum Monte Carlo (QMC) methods offer a unique way of solving the many-body problem non-perturbatively, providing feedback on features of nuclear interactions and addressing scenarios that are inaccessible to other approaches. Our contribution goes over two recent accomplishments in the theory of neutron matter: a) the fusing of QMC with chiral effective field theory interactions, focusing on local chiral 3N forces, and b) the first attempt to find an ab initio solution to the problem of static response.

  3. Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids

    NASA Astrophysics Data System (ADS)

    Holzmann, Markus; Clay, Raymond C.; Morales, Miguel A.; Tubman, Norm M.; Ceperley, David M.; Pierleoni, Carlo

    2016-07-01

    Concentrating on zero temperature quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one- and two-body correlation functions. We introduce effective procedures, such as using the potential and wave function split up into long and short range functions to simplify the method, and we discuss how to treat backflow wave functions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.

  4. Role of collisional broadening in Monte Carlo simulations of terahertz quantum cascade lasers

    SciTech Connect

    Matyas, Alpar; Lugli, Paolo; Jirauschek, Christian

    2013-01-07

    Using a generalized version of Fermi's golden rule, collisional broadening is self-consistently implemented into ensemble Monte Carlo carrier transport simulations, and its effect on the transport and optical properties of terahertz quantum cascade lasers is investigated. The inclusion of broadening yields improved agreement with the experiment, without a significant increase of the numerical load. Specifically, this effect is crucial for a correct modeling at low biases. In the lasing regime, broadening can lead to significantly reduced optical gain and output power, affecting the obtained current-voltage characteristics.

  5. Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature.

    PubMed

    Anagnostopoulos, Konstantinos N; Hanada, Masanori; Nishimura, Jun; Takeuchi, Shingo

    2008-01-18

    We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality. PMID:18232852

  6. Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

    SciTech Connect

    Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

    2014-10-01

    We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, a finding in stark contrast to DAC data.

  7. Auxiliary-field quantum Monte Carlo calculations for systems with long-range repulsive interactions

    SciTech Connect

    Silvestrelli, P.L.; Baroni, S.; Car, R. Scuola Internazionale Superiore di Studi Avanzati , via Beirut 2/4, I-34014 Trieste Institut Romand de Recherche Numerique en Physique des Materiaux , PHB Ecublens, CH-1015 Lausanne )

    1993-08-23

    We report on the first successful attempt to apply the auxiliary-field quantum Monte Carlo technique to the calculation of ground-state properties of systems of many electrons interacting via a Coulomb potential. We have been able to substantially reduce the huge statistical fluctuations arising from the repulsive, long-range character of the interactions, which had so far hindered the application of this method to [ital realistic] Hamiltonians for atoms, molecules, and solids. Our technique is demonstrated with calculations of ground-state properties of the simplest molecular and solid-state systems, i.e., the H[sub 2] molecule and the homogeneous electron gas.

  8. Quantum Monte Carlo method using phase-free random walks with slater determinants.

    PubMed

    Zhang, Shiwei; Krakauer, Henry

    2003-04-01

    We develop a quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants. An approximate approach is formulated with a trial wave function |Psi(T)> to control the phase problem. Using a plane-wave basis and nonlocal pseudopotentials, we apply the method to Be, Si, and P atoms and dimers, and to bulk Si supercells. Single-determinant wave functions from density functional theory calculations were used as |Psi(T)> with no additional optimization. The calculated binding energies of dimers and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results. PMID:12689312

  9. Ising nematic quantum critical point in a metal: a Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Lederer, Samuel

    The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to 24 × 24 sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP. With Yoni Schattner, Steven A. Kivelson, and Erez Berg.

  10. Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals.

    PubMed

    Berg, Erez; Metlitski, Max A; Sachdev, Subir

    2012-12-21

    The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical doping) are varied. Because of the strong coupling nature of this critical point and the "sign problem" plaguing numerical quantum Monte Carlo (QMC) methods, its theoretical understanding is still incomplete. Here, we show that the universal low-energy theory for the onset of antiferromagnetism in a metal can be realized in lattice models, which are free from the sign problem and hence can be simulated efficiently with QMC. Our simulations show Fermi surface reconstruction and unconventional spin-singlet superconductivity across the critical point. PMID:23258893

  11. Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems.

    PubMed

    Ma, Xiaoyao; Hall, Randall W; Löffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana

    2016-01-01

    The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem. PMID:26747795

  12. Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems

    NASA Astrophysics Data System (ADS)

    Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank; Kowalski, Karol; Bhaskaran-Nair, Kiran; Jarrell, Mark; Moreno, Juana

    2016-01-01

    The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

  13. Quantum Monte Carlo calculations of spectroscopic overlaps in A{<=}7 nuclei

    SciTech Connect

    Brida, I.; Pieper, Steven C.; Wiringa, R. B.

    2011-08-15

    We present Green's function Monte Carlo calculations of spectroscopic overlaps for A{<=}7 nuclei. The realistic Argonne v{sub 18} two-nucleon and Illinois-7 three-nucleon interactions are used to generate the nuclear states. The overlap matrix elements are extrapolated from mixed estimates between variational Monte Carlo and Green's function Monte Carlo wave functions. The overlap functions are used to obtain spectroscopic factors and asymptotic normalization coefficients, and they can serve as an input for reaction calculations.

  14. a Quantum Monte Carlo Study of the High Pressure Phases of Solid Hydrogen

    NASA Astrophysics Data System (ADS)

    Natoli, Vincent Dominic

    1994-01-01

    Variational and Diffusion Monte Carlo are powerful computational methods which can afford accurate estimates of the ground state properties of quantum many-body problems. We have applied these Monte Carlo methods to the high pressure phases of solid hydrogen to elucidate those parts of the phase diagram where experimental results are inconclusive or lacking. The method allows us to treat both electrons and protons as quantum particles by incorporating them in the trial wavefunction and avoids the Born-Oppenheimer and harmonic approximations. Our trial wavefunction uses single-body solutions from a mean-field calculation coupled with standard pair potential terms to achieve the most accurate results to date. Equally accurate results were realized for calculations in the disparate insulating molecular and metallic atomic regime. We performed a study of the possible ground state structures of the atomic metallic phase of hydrogen which identifies a new family of low energy atomic structures. Another study was done on the molecular phase over the range of pressures (40-180GPa) where recent experiments have observed spectral discontinuities and other interesting new phenomena. Particular attention was directed to determining the equation of state and orientational ordering. We find that molecular hydrogen adopts a lower symmetry insulating structure over a wide range of pressure. The results of the atomic and molecular studies are combined to draw conclusions about the molecular-atomic transition and other details about the high pressure phase diagram.

  15. Quantum Monte Carlo Assessment of the Relevance of Electronic Correlations in Defects and EOS in Metals

    SciTech Connect

    Hood, R Q; Williamson, A J; Dubois, J L; Reboredo, F A

    2008-02-07

    We have developed a highly accurate computational capability to calculate the equation of state (EOS) and defect formation energies of metallic systems. We are using a newly developed algorithm that enables the study of metallic systems with quantum Monte Carlo (QMC) methods. To date, technical limitations have restricted the application of QMC methods to semiconductors, insulators and the homogeneous electron gas. Using this new 'QMC for metals' we can determine, for the first time, the significance of correlation effects in the EOS and in the formation energies of point defects, impurities, surfaces and interfaces in metallic systems. These calculations go beyond the state-of-the-art accuracy which is currently obtained with Density Functional Theory approaches. Such benchmark calculations can provide more accurate predictions for the EOS and the formation energies of vacancies and interstitials in simple metals. These are important parameters in determining the mechanical properties as well as the micro-structural evolution of metals in irradiated materials or under extreme conditions. We describe the development of our 'QMC for metals' code, which has been adapted to run efficiently on a variety of computer architectures including BG/L. We present results of the first accurate quantum Monte Carlo calculation of an EOS of a realistic metallic system that goes beyond the homogeneous electron gas.

  16. Excited states from quantum Monte Carlo in the basis of Slater determinants

    SciTech Connect

    Humeniuk, Alexander; Mitrić, Roland

    2014-11-21

    Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excited states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will be required before the applicability of this method to electron correlation problems of interesting size can be assessed.

  17. Quantum Monte Carlo study of molecular polarization and antiferroelectric ordering in squaric acid crystals

    NASA Astrophysics Data System (ADS)

    Ishizuka, Hiroaki; Motome, Yukitoshi; Furukawa, Nobuo; Suzuki, Sei

    2011-08-01

    Effects of geometrical frustration and quantum fluctuation are theoretically investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded system, namely a squaric acid crystal. We elucidate the phase diagram for an effective model, the transverse-field Ising model on a frustrated checkerboard lattice, by using quantum Monte Carlo simulation. A crossover to a liquidlike paraelectric state with well-developed molecular polarizations is identified, distinguishably from long-range ordering. The emergence of long-range order from the liquidlike state exhibits peculiar aspects originating from the lifting of quasimacroscopic degeneracy, such as colossal enhancement of the transition temperature and a vanishingly small anomaly in the specific heat.

  18. Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

    SciTech Connect

    Zen, Andrea; Luo, Ye Mazzola, Guglielmo Sorella, Sandro; Guidoni, Leonardo

    2015-04-14

    Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.

  19. Chemically accurate description of aromatic rings interaction using quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Azadi, Sam

    We present an accurate study of interactions between benzene molecules using wave function based quantum Monte Carlo (QMC) methods. We compare our QMC results with density functional theory (DFT) using various van der Waals (vdW) functionals. This comparison enables us to tune vdW functionals. We show that highly optimizing the wave function and introducing more dynamical correlation into the wave function are crucial to calculate the weak chemical binding energy between benzene molecules. The good agreement among our results, experiments and quantum chemistry methods, is an important sign of the capability of the wave function based QMC methods to provide accurate description of very weak intermolecular interactions based on vdW dispersive forces.

  20. Torsional path integral Monte Carlo method for the quantum simulation of large molecules

    NASA Astrophysics Data System (ADS)

    Miller, Thomas F.; Clary, David C.

    2002-05-01

    A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.

  1. MORSE Monte Carlo code

    SciTech Connect

    Cramer, S.N.

    1984-01-01

    The MORSE code is a large general-use multigroup Monte Carlo code system. Although no claims can be made regarding its superiority in either theoretical details or Monte Carlo techniques, MORSE has been, since its inception at ORNL in the late 1960s, the most widely used Monte Carlo radiation transport code. The principal reason for this popularity is that MORSE is relatively easy to use, independent of any installation or distribution center, and it can be easily customized to fit almost any specific need. Features of the MORSE code are described.

  2. Aneesu-Rahman Prize Lecture: The ``sign problem'' in Quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Ceperley, D. M.

    1998-03-01

    Quantum simulation methods have been quite successful in giving exact results for certain systems, primarily bosons(Ceperley, D.M. , Rev. Mod. Phys. 67), 279 (1995).. Use of the same techniques in general quantum systems leads to the so-called ``sign problem''; the results are correct but the methods are very inefficient. There are two important questions to ask of a proposed method. Given enough computer time can arbitrarily accurate results be obtained? If so, how long does it take to achieve a given error? There are several methods (released-node or transient estimate) that are exact; the difficulty is in finding a method which also scales well with the number of quantum degrees of freedom. Exact methods, in general, scale exponentially with the number of fermions and in the inverse temperature (or accuracy). At root, the fact that wavefunction is complex or changes sign, gives rise to the poor scaling and the ``sign problem.'' It is not the fermion nature of the system, per se, that causes the difficulty. The desired state is not the absolute ground state. Methods which cancel random walks from positive and negative regions have also been limited to quite small systems because they scale poorly. There are a variety of approximate simulation methods which do scale well, such as variational Monte Carlo, and a variety of fixed-node methods (restricted Path Integral Monte Carlo at non-zero temperature and constrained path methods for lattice models) which fix only boundary conditions not the sampling function. For many systems, the variational and fixed-node methods can be very accurate. The lecture notes and references are on my group's homepage.

  3. Study of dispersion forces with quantum Monte Carlo: toward a continuum model for solvation.

    PubMed

    Amovilli, Claudio; Floris, Franca Maria

    2015-05-28

    We present a general method to compute dispersion interaction energy that, starting from London's interpretation, is based on the measure of the electronic electric field fluctuations, evaluated on electronic sampled configurations generated by quantum Monte Carlo. A damped electric field was considered in order to avoid divergence in the variance. Dispersion atom-atom C6 van der Waals coefficients were computed by coupling electric field fluctuations with static dipole polarizabilities. The dipole polarizability was evaluated at the diffusion Monte Carlo level by studying the response of the system to a constant external electric field. We extended the method to the calculation of the dispersion contribution to the free energy of solvation in the framework of the polarizable continuum model. We performed test calculations on pairs of some atomic systems. We considered He in ground and low lying excited states and Ne in the ground state and obtained a good agreement with literature data. We also made calculations on He, Ne, and F(-) in water as the solvent. Resulting dispersion contribution to the free energy of solvation shows the reliability of the method illustrated here. PMID:25535856

  4. Quantum Monte Carlo study of the reaction: C1 + CH3OH -->CH2OH+ HCl

    SciTech Connect

    Kollias, A.C.; Couronne, O.; Lester Jr., W.A.

    2003-12-01

    A theoretical study is reported of the Cl + CH{sub 3}OH {yields} CH{sub 2}OH + HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. Moller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.

  5. Correlated electron dynamics with time-dependent quantum Monte Carlo: three-dimensional helium.

    PubMed

    Christov, Ivan P

    2011-07-28

    Here the recently proposed time-dependent quantum Monte Carlo method is applied to three dimensional para- and ortho-helium atoms subjected to an external electromagnetic field with amplitude sufficient to cause significant ionization. By solving concurrently sets of up to 20,000 coupled 3D time-dependent Schrödinger equations for the guide waves and corresponding sets of first order equations of motion for the Monte Carlo walkers we obtain ground state energies in close agreement with the exact values. The combined use of spherical coordinates and B-splines along the radial coordinate proves to be especially accurate and efficient for such calculations. Our results for the dipole response and the ionization of an atom with un-correlated electrons are in good agreement with the predictions of the conventional time-dependent Hartree-Fock method while the calculations with correlated electrons show enhanced ionization that is due to the electron-electron repulsion. PMID:21806103

  6. Quantum Monte Carlo Study of the Reactions of CH with Acrolein: Major and Minor Channels.

    PubMed

    Pakhira, Srimanta; Singh, Ravi I; Olatunji-Ojo, Olayinka; Frenklach, Michael; Lester, William A

    2016-05-26

    Acrolein is an important unsaturated hydrocarbon, containing both C═O and C═C bonds, and responsible for atmospheric pollution. A recent study of major reactions of CH with acrolein has been supplemented with computations of other reactions of the system. Similar to the previous approach, the quantum Monte Carlo (QMC) method in the accurate diffusion Monte Carlo (DMC) method was implemented. Single determinant wave functions were used as trial functions for the random walks. Rate coefficients and product branching ratios were computed by solving master equations using the MultiWell software suite. At room temperature, the dominant product channels are 2-methylvinyl + CO (P6), 1,3-butadienal + H (P2), and furan + H (P1). At elevated temperatures, 2,3-butadienal + H (P10) is also a major product. The chain decomposition pathway to form C3H4 + HCO was not competitive with the cyclization pathway at any of the temperatures studied. The DMC branching fractions of the products formed in the subject reaction are in reasonable accord with previous experimental and theoretical values. The computed rate coefficients were found to be independent of pressure at temperatures relevant to combustion (1500-2500 K). PMID:27046018

  7. Accurate band gaps of semiconductors and insulators from Quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Nazarov, Roman; Hood, Randolph; Morales, Miguel

    2015-03-01

    Ab initio calculations are useful tools in developing materials with targeted band gaps for semiconductor industry. Unfortunately, the main workhorse of ab initio calculations - density functional theory (DFT) in local density approximation (LDA) or generalized gradient approximation (GGA) underestimates band gaps. Several approaches have been proposed starting from empirical corrections to more elaborate exchange-correlation functionals to deal with this problem. But none of these work well for the entire range of semiconductors and insulators. Deficiencies of DFT as a mean field method can be overcome using many-body techniques. Quantum Monte Carlo (QMC) methods can obtain a nearly exact numerical solutions of both total energies and spectral properties. Diffusion Monte Carlo (DMC), the most widely used QMC method, has been shown to provide gold standard results for different material properties, including spectroscopic constants of dimers and clusters, equation of state for solids, accurate descriptions of defects in metals and insulators. To test DMC's accuracy in a wider range of semiconductors and insulators we have computed band gaps of several semiconductors and insulators. We show that DMC can provide superior agreement with experiment compared with more traditional DFT approaches including high level exchange-correlation functionals (e.g. HSE).

  8. Quantum Monte Carlo study of the singlet-triplet transition in ethylene

    SciTech Connect

    El Akramine, Ouafae; Kollias, Alexander C.; Lester, Jr., William A.

    2003-01-23

    A theoretical study is reported of the transition between the ground state ({sup 1}A{sub g}) and the lowest triplet state (1{sup 3}B{sub 1u}) of ethylene based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using DMC trial functions constructed from Hartree-Fock, complete active space self-consistent field and multi-configuration self-consistent field wave functions, we have computed the atomization energy and the heat of formation of both states, and adiabatic and vertical energy differences between these states using both all-electron and effective core potential DMC. The ground state atomization energy and heat of formation are found to agree with experiment to within the error bounds of the computation and experiment. Predictions by DMC of the triplet state atomization energy and heat of formation are presented. The adiabatic singlet-triplet energy difference is found to differ by 5 kcal/mol from the value obtained in a recent photodissociation experiment.

  9. Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method

    NASA Astrophysics Data System (ADS)

    Sudheer, C. D.; Krishnan, S.; Srinivasan, A.; Kent, P. R. C.

    2013-02-01

    Diffusion Monte Carlo is a highly accurate Quantum Monte Carlo method for electronic structure calculations of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency on parallel machines. This step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receiving at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm: a simple renumbering of the MPI ranks based on proximity and a space filling curve significantly improves the MPI Allgather performance. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL show up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that require load balancing.

  10. Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method

    SciTech Connect

    Sudheer, C. D.; Krishnan, S.; Srinivasan, A.; Kent, P. R. C.

    2013-02-01

    Diffusion Monte Carlo is the most accurate widely used Quantum Monte Carlo method for the electronic structure of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency and avoid accumulation of systematic errors on parallel machines. The load balancing step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receiving at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL showing up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that requires load balancing.

  11. Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Parker, William D.; Umrigar, C. J.; Alfè, Dario; Petruzielo, F. R.; Hennig, Richard G.; Wilkins, John W.

    2015-04-01

    The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work by Williamson et al. (2001) [35] and Alfè and Gillan, (2004) [36] has demonstrated the reduction of the O (N3) cost of evaluating the Slater determinant with planewaves to O (N2) using localized basis functions. We compare four polynomial approximations as basis functions - interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO, and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.

  12. TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems

    NASA Astrophysics Data System (ADS)

    Seth, Priyanka; Krivenko, Igor; Ferrero, Michel; Parcollet, Olivier

    2016-03-01

    We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic electronic structure calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking.

  13. Monte Carlo variance reduction

    NASA Technical Reports Server (NTRS)

    Byrn, N. R.

    1980-01-01

    Computer program incorporates technique that reduces variance of forward Monte Carlo method for given amount of computer time in determining radiation environment in complex organic and inorganic systems exposed to significant amounts of radiation.

  14. Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer

    NASA Astrophysics Data System (ADS)

    Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

    2016-06-01

    Chemical accuracy is difficult to achieve for systems with transition metal atoms. Third row transition metal atoms are particularly challenging due to strong electron-electron correlation in localized d-orbitals. The Cr2 molecule is an outstanding example, which we previously treated with highly accurate auxiliary-field quantum Monte Carlo (AFQMC) calculations [W. Purwanto et al., J. Chem. Phys. 142, 064302 (2015)]. Somewhat surprisingly, computational description of the isoelectronic Mo2 dimer has also, to date, been scattered and less than satisfactory. We present high-level theoretical benchmarks of the Mo2 singlet ground state (X1Σg+) and first triplet excited state (a3Σu+), using the phaseless AFQMC calculations. Extrapolation to the complete basis set limit is performed. Excellent agreement with experimental spectroscopic constants is obtained. We also present a comparison of the correlation effects in Cr2 and Mo2.

  15. An auxiliary-field quantum Monte Carlo study of the chromium dimer

    SciTech Connect

    Purwanto, Wirawan Zhang, Shiwei; Krakauer, Henry

    2015-02-14

    The chromium dimer (Cr{sub 2}) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve (PEC), is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present an accurate calculation of the PEC and ground state properties of Cr{sub 2}, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set limit are then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.

  16. One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Matveeva, N.; Astrakharchik, G. E.

    2016-06-01

    A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.

  17. Lazy skip-lists: An algorithm for fast hybridization-expansion quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Sémon, P.; Yee, Chuck-Hou; Haule, Kristjan; Tremblay, A.-M. S.

    2014-08-01

    The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean field theory. In the strongly correlated regime, the method of choice for solving the impurity model is the hybridization-expansion continuous-time quantum Monte Carlo (CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: (a) skip lists and (b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with d electrons, we find speedups of ˜25 up to ˜500 compared to the direct evaluation of the matrix product. Even larger speedups are likely with f electron systems and with clusters of correlated atoms.

  18. Quantum Monte Carlo simulation of the ferroelectric or ferrielectric nanowire with core shell morphology

    NASA Astrophysics Data System (ADS)

    Feraoun, A.; Zaim, A.; Kerouad, M.

    2016-09-01

    By using the Quantum Monte Carlo simulation; the electric properties of a nanowire, consisting of a ferroelectric core of spin-1/2 surrounded by a ferroelectric shell of spin-1/2 with ferro- or anti-ferroelectric interfacial coupling have been studied within the framework of the Transverse Ising Model (TIM). We have examined the effects of the shell coupling Js, the interfacial coupling JInt, the transverse field Ω, and the temperature T on the hysteresis behavior and on the electric properties of the system. The remanent polarization and the coercive field as a function of the transverse field and the temperature are examined. A number of characteristic behavior have been found such as the appearance of triple hysteresis loops for appropriate values of the system parameters.

  19. Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application

    SciTech Connect

    Blunt, N. S. Kersten, J. A. F.; Smart, Simon D.; Spencer, J. S.; Booth, George H.; Alavi, Ali

    2015-05-14

    We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.

  20. Ground-state properties of LiH by reptation quantum Monte Carlo methods.

    PubMed

    Ospadov, Egor; Oblinsky, Daniel G; Rothstein, Stuart M

    2011-05-01

    We apply reptation quantum Monte Carlo to calculate one- and two-electron properties for ground-state LiH, including all tensor components for static polarizabilities and hyperpolarizabilities to fourth-order in the field. The importance sampling is performed with a large (QZ4P) STO basis set single determinant, directly obtained from commercial software, without incurring the overhead of optimizing many-parameter Jastrow-type functions of the inter-electronic and internuclear distances. We present formulas for the electrical response properties free from the finite-field approximation, which can be problematic for the purposes of stochastic estimation. The α, γ, A and C polarizability values are reasonably consistent with recent determinations reported in the literature, where they exist. A sum rule is obeyed for components of the B tensor, but B(zz,zz) as well as β(zzz) differ from what was reported in the literature. PMID:21445452

  1. Recent developments in auxiliary-field quantum Monte Carlo methods for cold atoms

    NASA Astrophysics Data System (ADS)

    Shi, Hao; Rosenberg, Peter; Vitali, Ettore; Chiesa, Simone; Zhang, Shiwei

    Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. We describe recent advances in auxiliary-field quantum Monte Carlo techniques, which eliminate an infinite variance problem in the standard algorithm, and improve both acceptance ratio and efficiency. The new methods enable calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. An equation of state is obtained, with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, condensate fraction, and pairing gap will be presented. The same methods are also applied to obtain exact results on the two-dimensional strongly interacting Fermi gas in the presence of Rashba spin-orbit (SOC), providing insights on the interplay between pairing and SOC. Supported by NSF, DOE, and the Simons Foundation.

  2. Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis

    NASA Astrophysics Data System (ADS)

    Vrbik, Jan; Ospadov, Egor; Rothstein, Stuart M.

    2016-07-01

    Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x'; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.

  3. Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application.

    PubMed

    Blunt, N S; Smart, Simon D; Kersten, J A F; Spencer, J S; Booth, George H; Alavi, Ali

    2015-05-14

    We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable. PMID:25978883

  4. Constrained-path quantum Monte Carlo approach for non-yrast states within the shell model

    NASA Astrophysics Data System (ADS)

    Bonnard, J.; Juillet, O.

    2016-04-01

    The present paper intends to present an extension of the constrained-path quantum Monte Carlo approach allowing to reconstruct non-yrast states in order to reach the complete spectroscopy of nuclei within the interacting shell model. As in the yrast case studied in a previous work, the formalism involves a variational symmetry-restored wave function assuming two central roles. First, it guides the underlying Brownian motion to improve the efficiency of the sampling. Second, it constrains the stochastic paths according to the phaseless approximation to control sign or phase problems that usually plague fermionic QMC simulations. Proof-of-principle results in the sd valence space are reported. They prove the ability of the scheme to offer remarkably accurate binding energies for both even- and odd-mass nuclei irrespective of the considered interaction.

  5. Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

    DOE PAGESBeta

    Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

    2014-10-01

    We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less

  6. Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

    PubMed

    Drummond, N D; Monserrat, Bartomeu; Lloyd-Williams, Jonathan H; López Ríos, P; Pickard, Chris J; Needs, R J

    2015-01-01

    Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases. PMID:26215251

  7. Benchmarking exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo

    SciTech Connect

    Clay, Raymond C.; Mcminis, Jeremy; McMahon, Jeffrey M.; Pierleoni, Carlo; Ceperley, David M.; Morales, Miguel A.

    2014-05-01

    The ab initio phase diagram of dense hydrogen is very sensitive to errors in the treatment of electronic correlation. Recently, it has been shown that the choice of the density functional has a large effect on the predicted location of both the liquid-liquid phase transition and the solid insulator-to-metal transition in dense hydrogen. To identify the most accurate functional for dense hydrogen applications, we systematically benchmark some of the most commonly used functionals using quantum Monte Carlo. By considering several measures of functional accuracy, we conclude that the van der Waals and hybrid functionals significantly outperform local density approximation and Perdew-Burke-Ernzerhof. We support these conclusions by analyzing the impact of functional choice on structural optimization in the molecular solid, and on the location of the liquid-liquid phase transition.

  8. Linear-scaling evaluation of the local energy in quantum MonteCarlo

    SciTech Connect

    Austin, Brian; Aspuru-Guzik, Alan; Salomon-Ferrer, Romelia; Lester Jr., William A.

    2006-02-11

    For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.

  9. Variational quantum Monte Carlo calculation of electronic and structural properties of crystals

    SciTech Connect

    Louie, S.G.

    1989-09-01

    Calculation of the electronic and structural properties of solids using a variational quantum Monte Carlo nonlocal pseudopotential approach is described. Ionization potentials and electron affinities for atoms, and binding energies and structural properties for crystals are found to be in very good agreement with experiment. The approach employs a correlated many-electron wavefunction of the Jastrow-Slater form and the exact Coulomb interaction between valence electrons. One- and two-body terms in the Jastrow factor are used and found necessary for an accurate description of the electron-electron energy for the systems considered. The method has further been applied to compute various single-particle properties for solids including the single-particle orbital occupancy, electron pair correlation functions, and quasiparticle excitation energies. 23 refs., 3 figs., 3 tabs.

  10. A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations

    SciTech Connect

    Nukala, Phani K. V. V.; Kent, P. R. C.

    2009-05-28

    We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N{sup 2}) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O(N{sup 2}) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN{sup 2}) work and O(MN{sup 2}) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.

  11. A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Nukala, Phani K. V. V.; Kent, P. R. C.

    2009-05-01

    We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N2) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O(N2) Sherman-Morrison algorithm for up to O(N ) updates. For multideterminant configuration-interaction-type trial wave functions of M +1 determinants, the new algorithm is significantly more efficient, saving both O(MN2) work and O(MN2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.

  12. Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Filippi, Claudia; Assaraf, Roland; Moroni, Saverio

    2016-05-01

    We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, in both all-electron and pseudopotential calculations.

  13. A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations.

    PubMed

    Nukala, Phani K V V; Kent, P R C

    2009-05-28

    We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N(2)) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O(N(2)) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN(2)) work and O(MN(2)) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions. PMID:19485435

  14. A Fast and efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations

    SciTech Connect

    Nukala, Phani K; Kent, Paul R

    2009-01-01

    We present an efficient low-rank updating algorithm for updating the trial wavefunctions used in Quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is $\\mathcal{O}(k N)$ during the $k$-th step compared with traditional algorithms that require $\\mathcal{O}(N^2)$ computations, where $N$ is the system size. For single determinant trial wavefunctions the new algorithm is faster than the traditional $\\mathcal{O}(N^2)$ Sherman-Morrison algorithm for up to $\\mathcal{O}(N)$ updates. For multideterminant configuration-interaction type trial wavefunctions of $M+1$ determinants, the new algorithm is significantly more efficient, saving both $\\mathcal{O}(MN^2)$ work and $\\mathcal{O}(MN^2)$ storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration interaction type wavefunctions.

  15. Quantum Monte Carlo study of charged transition-metal organometallic cluster systems

    NASA Astrophysics Data System (ADS)

    Tokar, Kamil; Derian, Rene; Stich, Ivan

    2015-03-01

    Using accurate fixed-node quantum Monte Carlo (QMC) methods we study 1D clusters formed by transition metal atoms separated by benzene molecules (TMBz), both positively and negatively charged. TMBz are among the most important π-bonded organometallics, which, however, often require charged states for experimental studies. We have performed a systematic study of ground-sate spin multiplets, ionization potentials, electron affinities, and dissociation energies of vanadium-benzene cationic and anionic half- and full-sandwiches. By comparison of QMC and DFT results, we find a very strong impact of electronic correlation on properties of these systems, such as dissociation energies, where ~1 eV energy corrections are found. In particular, the anions are unstable at the DFT level and are stabilized only at the QMC level after sophisticated optimization of the trial wavefunction. Supported by APVV-0207-11 and VEGA (2/0007/12) projects.

  16. Ferromagnetism of a repulsive atomic Fermi gas in an optical lattice: a quantum Monte Carlo study.

    PubMed

    Pilati, S; Zintchenko, I; Troyer, M

    2014-01-10

    Using continuous-space quantum Monte Carlo methods, we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and fully ferromagnetic phases. As the intensity of the optical lattice increases, the ferromagnetic instability takes place at weaker interactions, indicating a possible route to observe ferromagnetism in experiments performed with ultracold atoms. We compare our findings with previous predictions based on the standard computational method used in material science, namely density functional theory, and with results based on tight-binding models. PMID:24483906

  17. Phase Transition between Black and Blue Phosphorenes: A Quantum Monte Carlo Study

    NASA Astrophysics Data System (ADS)

    Li, Lesheng; Yao, Yi; Reeves, Kyle; Kanai, Yosuke

    Phase transition of the more common black phosphorene to blue phosphorene is of great interest because they are predicted to exhibit unique electronic and optical properties. However, these two phases are predicted to be separated by a rather large energy barrier. In this work, we study the transition pathway between black and blue phosphorenes by using the variable cell nudge elastic band method combined with density functional theory calculation. We show how diffusion quantum Monte Carlo method can be used for determining the energetics of the phase transition and demonstrate the use of two approaches for removing finite-size errors. Finally, we predict how applied stress can be used to control the energetic balance between these two different phases of phosphorene.

  18. An excited-state approach within full configuration interaction quantum Monte Carlo

    SciTech Connect

    Blunt, N. S.; Smart, Simon D.; Booth, George H.; Alavi, Ali

    2015-10-07

    We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

  19. Auxiliary-field based trial wave functions in quantum Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Chang, Chia-Chen; Rubenstein, Brenda; Morales, Miguel

    We propose a simple scheme for generating correlated multi-determinant trial wave functions for quantum Monte Carlo algorithms. The method is based on the Hubbard-Stratonovich transformation which decouples a two-body Jastrow-type correlator into one-body projectors coupled to auxiliary fields. We apply the technique to generate stochastic representations of the Gutzwiller wave function, and present benchmark resuts for the ground state energy of the Hubbard model in one dimension. Extensions of the proposed scheme to chemical systems will also be discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, 15-ERD-013.

  20. Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo.

    PubMed

    Filippi, Claudia; Assaraf, Roland; Moroni, Saverio

    2016-05-21

    We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, in both all-electron and pseudopotential calculations. PMID:27208934

  1. The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations

    SciTech Connect

    Sellier, J.M. Dimov, I.

    2014-09-15

    The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.

  2. Values of dimensional quantities from Monte Carlo calculations in quantum chromodynamics

    SciTech Connect

    Makeenko, Y.M.; Polikarpov, M.I.

    1983-10-25

    An expression is derived for ..lambda../sub L/(..beta..) to describe the behavior of the Monte Carlo data on the string tension coefficient in the transition region in the SU(3) lattice gauge theory. This expression leads to a 25% increase in ..lambda../sub mom/, while there are no changes in the other dimensional quantities (the deconfinement temperature, for example) found by the Monte Carlo method.

  3. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Clay, Raymond C.; Morales, Miguel A.

    2015-06-01

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

  4. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

    SciTech Connect

    Clay, Raymond C.; Morales, Miguel A.

    2015-06-21

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

  5. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo.

    PubMed

    Clay, Raymond C; Morales, Miguel A

    2015-06-21

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets. PMID:26093546

  6. Overcoming statistical error and bias in quantum Monte Carlo: Application to metal-doped helium clusters

    NASA Astrophysics Data System (ADS)

    Warren, Gary Lee, Jr.

    2005-11-01

    Quantum Monte Carlo (QMC) methods are a class of powerful computer simulation techniques for solving the many-body Schrodinger equation. These techniques deliver essentially exact results and boast favorable computational scaling with system size. Calculations provide a full quantum mechanical treatment and may be carried to arbitrary precision. These characteristics make QMC a promising choice for the investigation of doped helium clusters, where quantum effects are substantial. Stochastic in nature, QMC methods are susceptible to statistical bias and error, which must be carefully controlled. Moreover, the relationship between the finite sampling error and the statistical uncertainty in observables has never been systematically investigated. Estimates of arbitrary observables are often substandard and can be plagued by statistical uncertainties an order of magnitude or greater than those for corresponding estimates of the energy. In this work, we present an analysis of how finite populations, importance sampling, and dimensionality affect the statistical uncertainties in QMC estimates of arbitrary observables. We find that the uncertainty depends exponentially on the dimensionality of the system, independent of the observable or nature of the system. This provides insight into the minimal population sizes and importance sampling requirements necessary to obtain useful QMC estimates of properties in high-dimensional systems. With this understanding, we develop new, more robust energy optimization procedures for cluster wavefunctions. We also implement a high quality eight parameter ansatz for the investigation of both pure and doped helium cluster systems. Compared to exact DMC results, the optimized wavefunctions recover over 90% of the total energy for clusters of size n ≤ 20. Finally, we apply this knowledge directly to the study of the solvation behavior of neutral calcium and magnesium impurities in helium nanodroplets. Diffusion Monte Carlo calculations

  7. Optimization of a multideterminant wave function for quantum Monte Carlo: Li sub 2 ( X sup 1. Sigma. sup + sub g )

    SciTech Connect

    Sun, Z.; Barnett, R.N.; Lester, W.A. Jr. )

    1992-02-01

    A wave function constructed as a product of a four-determinant function and a symmetric correlation function is employed in Monte Carlo computations of the ground-state energy of Li{sub 2} at {ital R}{sub {ital e}} = 5.05 Bohrs. Wave function parameters are determined by a fixed-sample minimization of deviations of the local energy. Although the variational Monte Carlo energy for this function lies, as expected, below that of a similar wave function constructed with a single determinant, the four-determinant function/correlation function wave function gives no improvement in quantum Monte Carlo energy. However, the unoptimized four-determinant function/correlation function wave function does yield an energy in excellent agreement with the estimated exact result. The poorer energy of the optimized function is caused by degradation of the nodal structure during parameter optimization.

  8. Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo.

    PubMed

    Bouabça, Thomas; Braïda, Benoît; Caffarel, Michel

    2010-07-28

    A new type of electronic trial wavefunction suitable for quantum Monte Carlo calculations of molecular systems is presented. In contrast with the standard Jastrow-Slater form built with a unique global Jastrow term, it is proposed to introduce individual Jastrow factors attached to molecular orbitals. Such a form is expected to be more physical since it allows to describe differently the local electronic correlations associated with various molecular environments (1s-core orbitals, 3d-magnetic orbitals, localized two-center sigma-orbitals, delocalized pi-orbitals, atomic lone pairs, etc.). In contrast with the standard form, introducing different Jastrow terms allows us to change the nodal structure of the wavefunction, a point which is important in the context of building better nodes for more accurate fixed-node diffusion Monte Carlo (FN-DMC) calculations. Another important aspect resulting from the use of local Jastrow terms is the possibility of defining and preoptimizing local and transferable correlated units for building complex trial wavefunctions from simple parts. The practical aspects associated with the computation of the intricate derivatives of the multi-Jastrow trial function are presented in detail. Some first illustrative applications for atoms of increasing size (O, S, and Cu) and for the potential energy curve and spectroscopic constants of the FH molecule are presented. In the case of the copper atom, the use of the multi-Jastrow form at the variational Monte Carlo level has allowed us to improve significantly the value of the total ground-state energy (about 75% of the correlation energy with only one determinant and three atomic orbital Jastrow factors). In the case of the FH molecule (fluorine hydride), it has been found that the multi-Jastrow nodes lead to an almost exact FN-DMC value of the dissociation energy [D(0)=-140.7(4) kcal/mol instead of the estimated nonrelativistic Born-Oppenheimer exact value of -141.1], which is not the case

  9. Ab Initio Dynamical Correlations from Auxiliary-field quantum Monte Carlo: applications in the Hubbard model

    NASA Astrophysics Data System (ADS)

    Vitali, Ettore; Shi, Hao; Qin, Mingpu; Zhang, Shiwei

    The possibility of calculating dynamical correlation functions from first principles provides a unique opportunity to explore the manifold of the excited states of a quantum many-body system. Such calculations allow us to predict interesting physical properties like spectral functions, excitation spectra and charge and spin gaps, which are more difficult to access from usual equilibrium calculations. We address the ab-initio calculation of dynamical Green functions and two-body correlation functions in the Auxiliary-field Quantum Monte Carlo method, using the two-dimensional Hubbard model as an example. When the sign problem is not present, an unbiased estimation of imaginary time correlation functions is obtained. We discuss in detail the complexity and the stability of the calculations. Moreover, we propose a new approach which is expected to be very useful when dealing with dilute systems, e.g. for cold gases, allowing calculations with a very favorable complexity in the system size. Supported by NSF, DOE SciDAC, and Simons Foundation.

  10. Spin-orbit coupling in the strongly interacting Fermi gas: an exact quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Rosenberg, Peter; Shi, Hao; Chiesa, Simone; Zhang, Shiwei

    Spin-orbit coupling (SOC) plays an essential role in a variety of intriguing condensed matter phenomena, including the quantum Hall effect, and topological insulators and superconductors. The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the effects of SOC in a tunable, disorder-free system. Motivated by this experimental progress, we present here the first exact numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using auxiliary-field quantum Monte Carlo and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, study the spin behavior and momentum distribution, and examine the interplay of SOC and pairing in real and momentum space. Our results help illuminate the rich pairing structure induced by SOC, and provide important guidance to future experimental efforts. Supported by DOE SciDAC and NSF.

  11. Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

    NASA Astrophysics Data System (ADS)

    Shepherd, James J.; Booth, George H.; Alavi, Ali

    2012-06-01

    Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the "initiator" adaptation to full configuration interaction quantum Monte Carlo (i-FCIQMC), with a view to accelerating convergence. In particular, we find that the fixed-shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i-FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ⩽ rs ⩽ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38, and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed-shift strategy to reduce the computational cost of many i-FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

  12. State-of-the-art molecular applications of full configuration interaction quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Thomas, Robert; Overy, Catherine; Shepherd, James; Booth, George; Alavi, Ali

    2013-03-01

    Full configuration interaction quantum Monte Carlo (FCIQMC)1 and its initiator adaptation (i-FCIQMC)2 provide, in principle, exact (FCI) energies via a population dynamics algorithm of an ensemble of discrete, signed walkers in Slater-determinant space. We demonstrate that a novel choice of reference state has the potential to widen the scope of this already versatile method, and corroborate the finding that an extension of the algorithm to allow non-integer walkers can yield significantly reduced stochastic error without a commensurate increase in computational cost3. New applications of FCIQMC to transition-metal systems of general and biological interest are presented, many of which have, to date, posed serious challenges for traditional quantum chemical methods 45. 1 G. H. Booth, A. J. W. Thom, and A. Alavi, J. Chem. Phys., 131, 054106 (2009) 2 D. M. Cleland, G. H. Booth, and A. Alavi, J. Chem. Phys., 132, 041103 (2010) 3 F. R. Petruzielo, A. A. Holmes, H. J. Changlani, M. P. Nightingale and C. J. Umrigar, arXiv:1207.6138 4 N. B. Balabanov and K. A. Peterson, J. Chem. Phys., 125, 074110 (2006) 5 C. J. Cramer, M. Wloch, P. Piecuch, C. Puzzarini and L. Gagliardi, J. Phys. Chem. A, 110, 1991 (2006)

  13. Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model

    PubMed Central

    2015-01-01

    The penta-2,4-dieniminium cation (PSB3) displays similar ground state and first excited state potential energy features as those of the retinal protonated Schiff base (RPSB) chromophore in rhodopsin. Recently, PSB3 has been used to benchmark several electronic structure methods, including highly correlated multireference wave function approaches, highlighting the necessity to accurately describe the electronic correlation in order to obtain reliable properties even along the ground state (thermal) isomerization paths. In this work, we apply two quantum Monte Carlo approaches, the variational Monte Carlo and the lattice regularized diffusion Monte Carlo, to study the energetics and electronic properties of PSB3 along representative minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo is used in combination with the Jastrow antisymmetrized geminal power ansatz, which guarantees an accurate and balanced description of the static electronic correlation thanks to the multiconfigurational nature of the antisymmetrized geminal power term, and of the dynamical correlation, due to the presence of the Jastrow factor explicitly depending on electron–electron distances. Along the two ground state isomerization minimum energy paths of PSB3, CASSCF calculations yield wave functions having either charge transfer or diradical character in proximity of the two transition state configurations. Here, we observe that at the quantum Monte Carlo level of theory, only the transition state with charge transfer character can be located. The conical intersection, which becomes highly sloped, is observed only if the path connecting the two original CASSCF transition states is extended beyond the diradical one, namely by increasing the bond-length-alternation (BLA). These findings are in good agreement with the results obtained by MRCISD+Q calculations, and they demonstrate the importance of having an accurate description of the static and

  14. Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model.

    PubMed

    Zen, Andrea; Coccia, Emanuele; Gozem, Samer; Olivucci, Massimo; Guidoni, Leonardo

    2015-03-10

    The penta-2,4-dieniminium cation (PSB3) displays similar ground state and first excited state potential energy features as those of the retinal protonated Schiff base (RPSB) chromophore in rhodopsin. Recently, PSB3 has been used to benchmark several electronic structure methods, including highly correlated multireference wave function approaches, highlighting the necessity to accurately describe the electronic correlation in order to obtain reliable properties even along the ground state (thermal) isomerization paths. In this work, we apply two quantum Monte Carlo approaches, the variational Monte Carlo and the lattice regularized diffusion Monte Carlo, to study the energetics and electronic properties of PSB3 along representative minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo is used in combination with the Jastrow antisymmetrized geminal power ansatz, which guarantees an accurate and balanced description of the static electronic correlation thanks to the multiconfigurational nature of the antisymmetrized geminal power term, and of the dynamical correlation, due to the presence of the Jastrow factor explicitly depending on electron–electron distances. Along the two ground state isomerization minimum energy paths of PSB3, CASSCF calculations yield wave functions having either charge transfer or diradical character in proximity of the two transition state configurations. Here, we observe that at the quantum Monte Carlo level of theory, only the transition state with charge transfer character can be located. The conical intersection, which becomes highly sloped, is observed only if the path connecting the two original CASSCF transition states is extended beyond the diradical one, namely by increasing the bond-length-alternation (BLA). These findings are in good agreement with the results obtained by MRCISD+Q calculations, and they demonstrate the importance of having an accurate description of the static and

  15. Path Integral Quantum Monte Carlo Study of Coupling and Proximity Effects in Superfluid Helium-4

    NASA Astrophysics Data System (ADS)

    Graves, Max T.

    When bulk helium-4 is cooled below T = 2.18 K, it undergoes a phase transition to a superfluid, characterized by a complex wave function with a macroscopic phase and exhibits inviscid, quantized flow. The macroscopic phase coherence can be probed in a container filled with helium-4, by reducing one or more of its dimensions until they are smaller than the coherence length, the spatial distance over which order propagates. As this dimensional reduction occurs, enhanced thermal and quantum fluctuations push the transition to the superfluid state to lower temperatures. However, this trend can be countered via the proximity effect, where a bulk 3-dimensional (3d) superfluid is coupled to a low (2d) dimensional superfluid via a weak link producing superfluid correlations in the film at temperatures above the Kosterlitz-Thouless temperature. Recent experiments probing the coupling between 3d and 2d superfluid helium-4 have uncovered an anomalously large proximity effect, leading to an enhanced superfluid density that cannot be explained using the correlation length alone. In this work, we have determined the origin of this enhanced proximity effect via large scale quantum Monte Carlo simulations of helium-4 in a topologically non-trivial geometry that incorporates the important aspects of the experiments. We find that due to the bosonic symmetry of helium-4, identical particle permutations lead to correlations between contiguous spatial regions at a length scale greater than the coherence length. We show that quantum exchange plays a large role in explaining the anomalous experimental results while simultaneously showing how classical arguments fall short of this task.

  16. Quantum Monte Carlo calculations of electroweak transition matrix elements in A=6,7 nuclei

    SciTech Connect

    Pervin, Muslema; Pieper, Steven C.; Wiringa, R. B.

    2007-12-15

    Green's function Monte Carlo (GFMC) calculations of magnetic dipole, electric quadrupole, Fermi, and Gamow-Teller transition matrix elements are reported for A=6,7 nuclei. The matrix elements are extrapolated from mixed estimates that bracket the relevant electroweak operator between variational Monte Carlo (VMC) and GFMC propagated wave functions. Because they are off-diagonal terms, two mixed estimates are required for each transition, with a VMC initial (final) state paired with a GFMC final (initial) state. The realistic Argonne v{sub 18} two-nucleon and Illinois-2 three-nucleon interactions are used to generate the nuclear states. In most cases we find good agreement with experimental data.

  17. Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo.

    PubMed

    Kersten, J A F; Booth, George H; Alavi, Ali

    2016-08-01

    The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach. PMID:27497549

  18. Quantum and Molecular Mechanical (QM/MM) Monte Carlo Techniques for Modeling Condensed-Phase Reactions

    PubMed Central

    Jorgensen, Wiliiam L.

    2014-01-01

    A recent review (Acc. Chem. Res. 2010, 43:142–151) examined our use and development of a combined quantum and molecular mechanical (QM/MM) technique for modelling organic and enzymatic reactions. Advances included the PDDG/PM3 semiempirical QM (SQM) method, computation of multi-dimensional potentials of mean force (PMF), incorporation of on-the-fly QM in Monte Carlo simulations, and a polynomial quadrature method for rapidly treating proton-transfer reactions. The current article serves as a follow up on our progress. Highlights include new reactions, alternative SQM methods, a polarizable OPLS force field, and novel solvent environments, e.g., “on water” and room temperature ionic liquids. The methodology is strikingly accurate across a wide range of condensed-phase and antibody-catalyzed reactions including substitution, decarboxylation, elimination, isomerization, and pericyclic classes. Comparisons are made to systems treated with continuum-based solvents and ab initio or density functional theory (DFT) methods. Overall, the QM/MM methodology provides detailed characterization of reaction paths, proper configurational sampling, several advantages over implicit solvent models, and a reasonable computational cost. PMID:25431625

  19. A deterministic alternative to the full configuration interaction quantum Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Tubman, Norm M.; Lee, Joonho; Takeshita, Tyler Y.; Head-Gordon, Martin; Whaley, K. Birgitta

    2016-07-01

    Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for a wide range of systems, including the difficult Cr2 molecule. We demonstrate for systems like Cr2 that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. In addition our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C2.

  20. Quantum monte carlo study of the energetics of small hydrogenated and fluoride lithium clusters.

    PubMed

    Moreira, N L; Brito, B G A; Rabelo, J N Teixeira; Cândido, Ladir

    2016-06-30

    An investigation of the energetics of small lithium clusters doped either with a hydrogen or with a fluorine atom as a function of the number of lithium atoms using fixed-node diffusion quantum Monte Carlo (DMC) simulation is reported. It is found that the binding energy (BE) for the doped clusters increases in absolute values leading to a more stable system than for the pure ones in excellent agreement with available experimental measurements. The BE increases for pure, remains almost constant for hydrogenated, and decreases rapidly toward the bulk lithium for the fluoride as a function of the number of lithium atoms in the clusters. The BE, dissociation energy as well as the second difference in energy display a pronounced odd-even oscillation with the number of lithium atoms. The electron correlation inverts the odd-even oscillation pattern for the doped in comparison with the pure clusters and has an impact of 29%-83% to the BE being higher in the pure cluster followed by the hydrogenated and then by the fluoride. The dissociation energy and the second difference in energy indicate that the doped cluster Li3 H is the most stable whereas among the pure ones the more stable are Li2 , Li4 , and Li6 . The electron correlation energy is crucial for the stabilization of Li3 H. © 2016 Wiley Periodicals, Inc. PMID:26992447

  1. Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

    NASA Astrophysics Data System (ADS)

    Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Miguel A.

    2016-01-01

    An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though density-functional-theory-based first-principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo (QMC) -based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC-based force estimators and use them to gain insight into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP, and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and we estimate the magnitudes of these effects when possible.

  2. Quantum Monte Carlo for large chemical systems: implementing efficient strategies for petascale platforms and beyond.

    PubMed

    Scemama, Anthony; Caffarel, Michel; Oseret, Emmanuel; Jalby, William

    2013-04-30

    Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible. PMID:23288704

  3. Properties of Solar Thermal Fuels by Accurate Quantum Monte Carlo Calculations

    NASA Astrophysics Data System (ADS)

    Saritas, Kayahan; Ataca, Can; Grossman, Jeffrey C.

    2014-03-01

    Efficient utilization of the sun as a renewable and clean energy source is one of the major goals of this century due to increasing energy demand and environmental impact. Solar thermal fuels are materials that capture and store the sun's energy in the form of chemical bonds, which can then be released as heat on demand and charged again. Previous work on solar thermal fuels faced challenges related to the cyclability of the fuel over time, as well as the need for higher energy densities. Recently, it was shown that by templating photoswitches onto carbon nanostructures, both high energy density as well as high stability can be achieved. In this work, we explore alternative molecules to azobenzene in such a nano-templated system. We employ the highly accurate quantum Monte Carlo (QMC) method to predict the energy storage potential for each molecule. Our calculations show that in many cases the level of accuracy provided by density functional theory (DFT) is sufficient. However, in some cases, such as dihydroazulene, the drastic change in conjugation upon light absorption causes the DFT predictions to be inconsistent and incorrect. For this case, we compare our QMC results for the geometric structure, band gap and reaction enthalpy with different DFT functionals.

  4. Quantum Monte Carlo simulations of Ti4 O7 Magnéli phase

    NASA Astrophysics Data System (ADS)

    Benali, Anouar; Shulenburger, Luke; Krogel, Jaron; Zhong, Xiaoliang; Kent, Paul; Heinonen, Olle

    2015-03-01

    Ti4O7 is ubiquitous in Ti-oxides. It has been extensively studied, both experimentally and theoretically in the past decades using multiple levels of theories, resulting in multiple diverse results. The latest DFT +SIC methods and state of the art HSE06 hybrid functionals even propose a new anti-ferromagnetic state at low temperature. Using Quantum Monte Carlo (QMC), as implemented in the QMCPACK simulation package, we investigated the electronic and magnetic properties of Ti4O7 at low (120K) and high (298K) temperatures and at different magnetic states. This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. L.S, J.K and P.K were supported through Predictive Theory and Modeling for Materials and Chemical Science program by the Office of Basic Energy Sciences (BES), Department of Energy (DOE) Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.

  5. Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

    SciTech Connect

    Thomas, Robert E.; Overy, Catherine; Opalka, Daniel; Alavi, Ali; Knowles, Peter J.; Booth, George H.

    2015-08-07

    Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.

  6. Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

    DOE PAGESBeta

    Kung, Y. F.; Chen, C. -C.; Wang, Yao; Huang, E. W.; Nowadnick, E. A.; Moritz, B.; Scalettar, R. T.; Johnston, S.; Devereaux, T. P.

    2016-04-29

    Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

  7. Diffusion Quantum Monte Carlo predictions for bulk MnNiO3

    NASA Astrophysics Data System (ADS)

    Mitra, Chandrima; Krogel, Jaron; Reboredo, Fernando A.

    MnNiO3 is a strongly correlated transition metal oxide that has recently been investigated theoretically for its potential application as an oxygen-evolution photo-catalyst. However, there is no experimental report on critical quantities like its band gap or its bulk modulus. Recent theoretical predictions with standard functionals, such as PBE +U and HSE show large discrepancies in the band-gaps (about 1.23 eV), depending on the nature of the functional used. Hence, there is clearly a need for an accurate quantitative prediction of the band-gap in order to decide its usefulness as a photo-catalyst. In this work, we present Diffusion Quantum Monte Carlo (DMC) study of the bulk properties of MnNiO3. This includes the quasiparticle band gap for the two spin channels, the equilibrium lattice parameter and the bulk modulus. The DMC approach has already been shown to achieve excellent agreement with experimental results for other oxides such as ZnO NiO and Fe2O3. To our knowledge, MnNiO3 is the first case where this theory is applied before experiments are done. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

  8. An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Booth, George H.; Cleland, Deidre; Alavi, Ali; Tew, David P.

    2012-10-01

    By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the { [2]_{{R12}} } approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.

  9. The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem

    NASA Astrophysics Data System (ADS)

    Kolodrubetz, M. H.; Spencer, J. S.; Clark, B. K.; Foulkes, W. M. C.

    2013-01-01

    The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.

  10. Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo.

    PubMed

    Cleland, Deidre; Booth, George H; Alavi, Ali

    2010-01-28

    We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N(2) molecule as an illustration, we show that rather small initiator spaces and numbers of walkers can converge with submilliHartree accuracy to the known full configuration-interaction (FCI) energy (in the cc-pVDZ basis), in both the equilibrium geometry and the multiconfigurational stretched case. We use the same method to compute the energy with cc-pVTZ and cc-pVQZ basis sets, the latter having an FCI space of over 10(15) with very modest computational resources. PMID:20113011

  11. Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Cleland, Deidre; Booth, George H.; Alavi, Ali

    2010-01-01

    We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N2 molecule as an illustration, we show that rather small initiator spaces and numbers of walkers can converge with submilliHartree accuracy to the known full configuration-interaction (FCI) energy (in the cc-pVDZ basis), in both the equilibrium geometry and the multiconfigurational stretched case. We use the same method to compute the energy with cc-pVTZ and cc-pVQZ basis sets, the latter having an FCI space of over 1015 with very modest computational resources.

  12. Optimized Non-Orthogonal Localized Orbitals for Linear Scaling Quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Williamson, Andrew; Reboredo, Fernando; Galli, Giulia

    2004-03-01

    It has been shown [1] that Quantum Monte Carlo calculations of total energies of interacting systems can be made to scale nearly linearly with the number of electrons (N), by using localized single particle orbitals to construct Slater determinants. Here we propose a new way of defining the localized orbitals required for O(N)-QMC calculation, by minimizing an appropriate cost function yielding a set of N non-orthogonal (NO) localized orbitals considerably smoother in real space than Maximally localized Wannier functions (MLWF). These NO orbitals have better localization properties than MLWFs. We show that for semiconducting systems NO orbitals can be localized in a much smaller region of space than orthogonal orbitals (typically, one eighth of the volume) and give total energies with the same accuracy, thus yielding a linear scaling QMC algorithm which is 5 times faster than the one originally proposed [1]. We also discuss the extension of O(N)-QMC with NO orbitals to the calculations of total energies of metallic systems. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. [1] A. J. Williamson, R.Q. Hood and J.C. Grossman, Phys. Rev. Lett. 87, 246406 (2001)

  13. Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

    DOE PAGESBeta

    Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Maguel A.

    2016-01-19

    An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based rst principles methods have the potential to provide the accuracy and computational e ciency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quanti cation of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures atmore » thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by di erent density functionals. We nd that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative di erences exhibited by the major classes of functionals, and estimate the magnitudes of these e ects when possible.« less

  14. Schwarzschild Radius from Monte Carlo Calculation of the Wilson Loop in Supersymmetric Matrix Quantum Mechanics

    SciTech Connect

    Hanada, Masanori; Miwa, Akitsugu; Nishimura, Jun; Takeuchi, Shingo

    2009-05-08

    In the string-gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop W in gauge theory is expected to contain the information of the Schwarzschild radius R{sub Sch} of the dual black hole geometry as log=R{sub Sch}/(2{pi}{alpha}{sup '}T). This translates to the power-law behavior log=1.89(T/{lambda}{sup 1/3}){sup -3/5}, where {lambda} is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulations of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as {alpha}{sup '} corrections on the gravity side. Our conclusion also demonstrates manifestly the fuzzball picture of black holes.

  15. Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Kung, Y. F.; Chen, C.-C.; Wang, Yao; Huang, E. W.; Nowadnick, E. A.; Moritz, B.; Scalettar, R. T.; Johnston, S.; Devereaux, T. P.

    2016-04-01

    We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π ,π ) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.

  16. Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics.

    PubMed

    Hanada, Masanori; Miwa, Akitsugu; Nishimura, Jun; Takeuchi, Shingo

    2009-05-01

    In the string-gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop W in gauge theory is expected to contain the information of the Schwarzschild radius RSch of the dual black hole geometry as log(W)=RSch/(2pialpha'T). This translates to the power-law behavior log(W)=1.89(T/lambda 1/3)-3/5, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulations of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side. Our conclusion also demonstrates manifestly the fuzzball picture of black holes. PMID:19518857

  17. Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Kersten, J. A. F.; Booth, George H.; Alavi, Ali

    2016-08-01

    The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.

  18. Bond Breaking of Simple Molecules in Auxiliary-Field Quantum Monte Carlo with GVB Wave Functions

    NASA Astrophysics Data System (ADS)

    Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei; Al-Saidi, Wissam

    2007-03-01

    Accurate potential energy curves are an essential ingredient in understanding chemical reactions. This problem spans a wide range of correlations, with correlation effects being the most important in the bond-breaking regime. We report potential energy curves of simple molecules, including water and the carbon dimer, within the framework of the auxiliary-field quantum Monte Carlo (AFQMC) method. AFQMC projects the many-body ground-state from a trial wave function, which is also used to control the sign/phase problem. A previous calculation showed that AFQMC could provide a fairly uniform description of the bond stretching of a water molecule, even with a simple unrestricted Hartree-Fock (UHF) trial wave function. We investigate the use of Generalized Valence Bond (GVB). GVB gives a better description of the molecule than UHF; so it is a simple yet efficient alternative to using a single Slater determinant trial wave function. We will compare AFQMC results with other correlated methods and the exact configuration interaction calculations. Al-Saidi, Zhang, Krakauer, J. Chem. Phys. 124, 224101 (2006)

  19. Study of Atoms and Molecules with Auxiliary-Field Quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Purwanto, Wirawan; Suewattana, Malliga; Krakauer, Henry; Zhang, Shiwei; Walter, Eric J.

    2006-03-01

    We study the ground-state properties of second-row atoms and molecules using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method projects the many-body ground state from a trial wave function by means of random walks in the Slater-determinant space. We use a single Slater-determinant trial wave function obtained from density-functional theory (DFT) or Hartree-Fock (HF) calculations. The calculations were done with a plane-wave basis and supercells with periodic boundary condition. We investigate the finite-size effects and the accuracy of pseudopotentials within DFT, HF, and AF QMC frameworks. Pseudopotentials generated from both LDA (OPIUM) and HF are employed. We find that the many-body QMC calculations show a greater sensitivity to the accuracy of the pseudopotentials. With reliable pseudopotentials, the ionization potentials and dissociation energies obtained using AF QMC are in excellent agreement with the experimental results. S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003) http://opium.sourceforge.net I. Ovcharenko, A. Aspuru-Guzik, and W. A. Lester, J. Chem. Phys. 114, 7790 (2001)

  20. Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis.

    PubMed

    Al-Saidi, W A; Zhang, Shiwei; Krakauer, Henry

    2006-06-14

    We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in H(2)O, our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T). PMID:16784257

  1. A study of electron affinities using the initiator approach to full configuration interaction quantum Monte Carlo.

    PubMed

    Cleland, D M; Booth, George H; Alavi, Ali

    2011-01-14

    For the atoms with Z ≤ 11, energies obtained using the "initiator" extension to full configuration interaction quantum Monte Carlo (i-FCIQMC) come to within statistical errors of the FCIQMC results. As these FCIQMC values have been shown to converge onto FCI results, the i-FCIQMC method allows similar accuracy to be achieved while significantly reducing the scaling with the size of the Slater determinant space. The i-FCIQMC electron affinities of the Z ≤ 11 atoms in the aug-cc-pVXZ basis sets are presented here. In every case, values are obtained to well within chemical accuracy [the mean absolute deviation (MAD) from the relativistically corrected experimental values is 0.41 mE(h)], and significantly improve on coupled cluster with singles, doubles and perturbative triples [CCSD(T)] results. Since the only remaining source of error is basis set incompleteness, we have investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results. By doing so, much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials presented in a previous paper. With this F12 correction, the MAD can be further reduced to 0.13 mE(h) for the electron affinities and 0.31 mE(h) for the ionization potentials. PMID:21241085

  2. Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

    SciTech Connect

    Al-Saidi, W.A.; Zhang Shiwei; Krakauer, Henry

    2006-06-14

    We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schroedinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in H{sub 2}O, our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T)

  3. Symmetry Breaking and Broken Ergodicity in Full Configuration Interaction Quantum Monte Carlo.

    PubMed

    Thomas, Robert E; Overy, Catherine; Booth, George H; Alavi, Ali

    2014-05-13

    The initiator full configuration interaction quantum Monte Carlo method (i-FCIQMC) is applied to the binding curve of N2 in Slater-determinant Hilbert spaces formed of both canonical restricted Hartree-Fock (RHF) and symmetry-broken unrestricted Hartree-Fock (UHF) orbitals. By explicit calculation, we demonstrate that the technique yields the same total energy for both types of orbital but that as the bond is stretched, FCI expansions expressed in unrestricted orbitals are substantially more compact than their restricted counterparts and more compact than those expressed in split-localized orbitals. These unrestricted Hilbert spaces, however, become nonergodic toward the dissociation limit, and the total wave function may be thought of as the sum of two weakly coupled, spin-impure, functions whose energies are nonetheless very close to the exact energy. In this limit, it is a challenge for i-FCIQMC to resolve a spin-pure wave function. The use of unrestricted natural orbitals is a promising remedy for this problem, as their expansions are more strongly weighted toward lower excitations of the reference, and they provide stronger coupling to higher excitations than do UHF orbitals. PMID:26580521

  4. N-(sulfoethyl) iminodiacetic acid-based lanthanide coordination polymers: Synthesis, magnetism and quantum Monte Carlo studies

    SciTech Connect

    Zhuang Guilin; Chen Wulin; Zheng Jun; Yu Huiyou; Wang Jianguo

    2012-08-15

    A series of lanthanide coordination polymers have been obtained through the hydrothermal reaction of N-(sulfoethyl) iminodiacetic acid (H{sub 3}SIDA) and Ln(NO{sub 3}){sub 3} (Ln=La, 1; Pr, 2; Nd, 3; Gd, 4). Crystal structure analysis exhibits that lanthanide ions affect the coordination number, bond length and dimension of compounds 1-4, which reveal that their structure diversity can be attributed to the effect of lanthanide contraction. Furthermore, the combination of magnetic measure with quantum Monte Carlo(QMC) studies exhibits that the coupling parameters between two adjacent Gd{sup 3+} ions for anti-anti and syn-anti carboxylate bridges are -1.0 Multiplication-Sign 10{sup -3} and -5.0 Multiplication-Sign 10{sup -3} cm{sup -1}, respectively, which reveals weak antiferromagnetic interaction in 4. - Graphical abstract: Four lanthanide coordination polymers with N-(sulfoethyl) iminodiacetic acid were obtained under hydrothermal condition and reveal the weak antiferromagnetic coupling between two Gd{sup 3+} ions by Quantum Monte Carlo studies. Highlights: Black-Right-Pointing-Pointer Four lanthanide coordination polymers of H{sub 3}SIDA ligand were obtained. Black-Right-Pointing-Pointer Lanthanide ions play an important role in their structural diversity. Black-Right-Pointing-Pointer Magnetic measure exhibits that compound 4 features antiferromagnetic property. Black-Right-Pointing-Pointer Quantum Monte Carlo studies reveal the coupling parameters of two Gd{sup 3+} ions.

  5. Quantum Monte Carlo study of quasi-one-dimensional Bose gases

    NASA Astrophysics Data System (ADS)

    Astrakharchik, G. E.; Blume, D.; Giorgini, S.; Granger, B. E.

    2004-04-01

    We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks-Girardeau regime for a critical value of the 3D scattering length a3D; (iii) enters a unitary regime for |a3D| rarr infin, where the properties of the gas are independent of a3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.

  6. Ab initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

    NASA Astrophysics Data System (ADS)

    Dornheim, T.; Groth, S.; Schoof, T.; Hann, C.; Bonitz, M.

    2016-05-01

    In a recent publication [S. Groth et al., Phys. Rev. B 93, 085102 (2016), 10.1103/PhysRevB.93.085102], we have shown that the combination of two complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015), 10.1103/PhysRevLett.115.130402] and permutation blocking path integral Monte Carlo [T. Dornheim et al., New J. Phys. 17, 073017 (2015), 10.1088/1367-2630/17/7/073017], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires nontrivial enhancements that we describe in detail. We compare our simulation results with recent restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013), 10.1103/PhysRevLett.110.146405] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.

  7. Shell model Monte Carlo methods

    SciTech Connect

    Koonin, S.E.; Dean, D.J.

    1996-10-01

    We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of {gamma}-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs.

  8. Monte Carlo Event Generators

    NASA Astrophysics Data System (ADS)

    Dytman, Steven

    2011-10-01

    Every neutrino experiment requires a Monte Carlo event generator for various purposes. Historically, each series of experiments developed their own code which tuned to their needs. Modern experiments would benefit from a universal code (e.g. PYTHIA) which would allow more direct comparison between experiments. GENIE attempts to be that code. This paper compares most commonly used codes and provides some details of GENIE.

  9. Structural stability and defect energetics of ZnO from diffusion quantum Monte Carlo

    SciTech Connect

    Santana, Juan A.; Krogel, Jaron T.; Kim, Jeongnim; Reboredo, Fernando A.; Kent, Paul R. C.

    2015-04-28

    We have applied the many-body ab initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure and the energetics of the oxygen vacancy, zinc interstitial, and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory (DFT) approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O{sub 2}, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy as a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.

  10. Towards prediction of correlated material properties using quantum Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Wagner, Lucas

    Correlated electron systems offer a richness of physics far beyond noninteracting systems. If we would like to pursue the dream of designer correlated materials, or, even to set a more modest goal, to explain in detail the properties and effective physics of known materials, then accurate simulation methods are required. Using modern computational resources, quantum Monte Carlo (QMC) techniques offer a way to directly simulate electron correlations. I will show some recent results on a few extremely challenging materials including the metal-insulator transition of VO2, the ground state of the doped cuprates, and the pressure dependence of magnetic properties in FeSe. By using a relatively simple implementation of QMC, at least some properties of these materials can be described truly from first principles, without any adjustable parameters. Using the QMC platform, we have developed a way of systematically deriving effective lattice models from the simulation. This procedure is particularly attractive for correlated electron systems because the QMC methods treat the one-body and many-body components of the wave function and Hamiltonian on completely equal footing. I will show some examples of using this downfolding technique and the high accuracy of QMC to connect our intuitive ideas about interacting electron systems with high fidelity simulations. The work in this presentation was supported in part by NSF DMR 1206242, the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program under Award Number FG02-12ER46875, and the Center for Emergent Superconductivity, Department of Energy Frontier Research Center under Grant No. DEAC0298CH1088. Computing resources were provided by a Blue Waters Illinois grant and INCITE PhotSuper and SuperMatSim allocations.

  11. Structural Stability and Defect Energetics of ZnO from Diffusion Quantum Monte Carlo

    DOE PAGESBeta

    Santana Palacio, Juan A.; Krogel, Jaron T.; Kim, Jeongnim; Kent, Paul R.; Reboredo, Fernando A.

    2015-04-28

    We have applied the many-body ab-initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure, and the energetics of the oxygen vacancy, zinc interstitial and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O2, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy asmore » a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type, and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.« less

  12. Structural Stability and Defect Energetics of ZnO from Diffusion Quantum Monte Carlo

    SciTech Connect

    Santana Palacio, Juan A.; Krogel, Jaron T.; Kim, Jeongnim; Kent, Paul R.; Reboredo, Fernando A.

    2015-04-28

    We have applied the many-body ab-initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure, and the energetics of the oxygen vacancy, zinc interstitial and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O2, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy as a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type, and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.

  13. Quantum Monte Carlo Benchmark of Exchange-Correlation Functionals for Bulk Water.

    PubMed

    Morales, Miguel A; Gergely, John R; McMinis, Jeremy; McMahon, Jeffrey M; Kim, Jeongnim; Ceperley, David M

    2014-06-10

    The accurate description of the thermodynamic and dynamical properties of liquid water from first-principles is a very important challenge to the theoretical community. This represents not only a critical test of the predictive capabilities of first-principles methods, but it will also shed light into the microscopic properties of such an important substance. Density Functional Theory, the main workhorse in the field of first-principles methods, has been so far unable to properly describe water and its unusual properties in the liquid state. With the recent introduction of exact exchange and an improved description of dispersion interaction, the possibility of an accurate description of the liquid is finally within reach. Unfortunately, there is still no way to systematically improve exchange-correlation functionals, and the number of available functionals is very large. In this article we use highly accurate quantum Monte Carlo calculations to benchmark a selection of exchange-correlation functionals typically used in Density Functional Theory simulations of bulk water. This allows us to test the predictive capabilities of these functionals in water, giving us a way to choose optimal functionals for first-principles simulations. We compare and contrast the importance of different features of functionals, including the hybrid component, the vdW component, and their importance within different aspects of the PES. In addition, in order to correct the inaccuracies in the description of short-range interactions in the liquid, we test a recently introduced scheme that combines Density Functional Theory with Coupled Cluster calculations through a Many-Body expansion of the energy. PMID:26580755

  14. Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations

    SciTech Connect

    Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian

    2006-10-01

    An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.

  15. Quantum mechanical single molecule partition function from path integral Monte Carlo simulations.

    PubMed

    Chempath, Shaji; Predescu, Cristian; Bell, Alexis T

    2006-06-21

    An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented. PMID:16821901

  16. Quantum Monte Carlo calculations of structural properties of FeO under pressure.

    PubMed

    Kolorenc, Jindrich; Mitas, Lubos

    2008-10-31

    We determine the equation of state of stoichiometric FeO by employing the diffusion Monte Carlo method. The fermionic nodes are fixed by a single Slater determinant of spin-unrestricted orbitals. The calculated ambient-pressure properties (lattice constant, bulk modulus, and cohesive energy) agree very well with available experimental data. At approximately 65 GPa, the atomic lattice changes from the rocksalt B1 to the NiAs-type inverse B8 structure. PMID:18999838

  17. Retrodictive derivation of the radical-ion-pair master equation and Monte Carlo simulation with single-molecule quantum trajectories.

    PubMed

    Kritsotakis, M; Kominis, I K

    2014-10-01

    Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach. PMID:25375535

  18. Retrodictive derivation of the radical-ion-pair master equation and Monte Carlo simulation with single-molecule quantum trajectories

    NASA Astrophysics Data System (ADS)

    Kritsotakis, M.; Kominis, I. K.

    2014-10-01

    Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011), 10.1103/PhysRevE.83.056118]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

  19. Quantum effects in a free-standing graphene lattice: Path-integral against classical Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Brito, B. G. A.; Cândido, Ladir; Hai, G.-Q.; Peeters, F. M.

    2015-11-01

    In order to study quantum effects in a two-dimensional crystal lattice of a free-standing monolayer graphene, we have performed both path-integral Monte Carlo (PIMC) and classical Monte Carlo (MC) simulations for temperatures up to 2000 K. The REBO potential is used for the interatomic interaction. The total energy, interatomic distance, root-mean-square displacement of the atom vibrations, and the free energy of the graphene layer are calculated. The obtained lattice vibrational energy per atom from the classical MC simulation is very close to the energy of a three-dimensional harmonic oscillator 3 kBT . The PIMC simulation shows that quantum effects due to zero-point vibrations are significant for temperatures T <1000 K. The quantum contribution to the lattice vibrational energy becomes larger than that of the classical lattice for T <400 K. The lattice expansion due to the zero-point motion causes an increase of 0.53% in the lattice parameter. A minimum in the lattice parameter appears at T ≃500 K. Quantum effects on the atomic vibration amplitude of the graphene lattice and its free energy are investigated.

  20. Monte Carlo portal dosimetry

    SciTech Connect

    Chin, P.W. . E-mail: mary.chin@physics.org

    2005-10-15

    This project developed a solution for verifying external photon beam radiotherapy. The solution is based on a calibration chain for deriving portal dose maps from acquired portal images, and a calculation framework for predicting portal dose maps. Quantitative comparison between acquired and predicted portal dose maps accomplishes both geometric (patient positioning with respect to the beam) and dosimetric (two-dimensional fluence distribution of the beam) verifications. A disagreement would indicate that beam delivery had not been according to plan. The solution addresses the clinical need for verifying radiotherapy both pretreatment (without the patient in the beam) and on treatment (with the patient in the beam). Medical linear accelerators mounted with electronic portal imaging devices (EPIDs) were used to acquire portal images. Two types of EPIDs were investigated: the amorphous silicon (a-Si) and the scanning liquid ion chamber (SLIC). The EGSnrc family of Monte Carlo codes were used to predict portal dose maps by computer simulation of radiation transport in the beam-phantom-EPID configuration. Monte Carlo simulations have been implemented on several levels of high throughput computing (HTC), including the grid, to reduce computation time. The solution has been tested across the entire clinical range of gantry angle, beam size (5 cmx5 cm to 20 cmx20 cm), and beam-patient and patient-EPID separations (4 to 38 cm). In these tests of known beam-phantom-EPID configurations, agreement between acquired and predicted portal dose profiles was consistently within 2% of the central axis value. This Monte Carlo portal dosimetry solution therefore achieved combined versatility, accuracy, and speed not readily achievable by other techniques.

  1. Creation of a GUI for Zori, a Quantum Monte Carlo program, usingRappture

    SciTech Connect

    Olivares-Amaya, R.; Salomon Ferrer, R.; Lester Jr., W.A.; Amador-Bedolla, C.

    2007-12-01

    In their research laboratories, academic institutions produce some of the most advanced software for scientific applications. However, this software is usually developed only for local application in the research laboratory or for method development. In spite of having the latest advances in the particular field of science, such software often lacks adequate documentation and therefore is difficult to use by anyone other than the code developers. As such codes become more complex, so typically do the input files and command statements necessary to operate them. Many programs offer the flexibility of performing calculations based on different methods that have their own set of variables and options to be specified. Moreover, situations can arise in which certain options are incompatible with each other. For this reason, users outside the development group can be unaware of how the program runs in detail. The opportunity can be lost to make the software readily available outside of the laboratory of origin. This is a long-standing problem in scientific programming. Rappture, Rapid Application Infrastructure [1], is a new GUI development kit that enables a developer to build an I/O interface for a specific application. This capability enables users to work only with the generated GUI and avoids the problem of the user needing to learn details of the code. Further, it reduces input errors by explicitly specifying the variables required. Zori, a quantum Monte Carlo (QMC) program, developed by the Lester group at the University of California, Berkeley [2], is one of the few free tools available for this field. Like many scientific computer packages, Zori suffers from the problems described above. Potential users outside the research group have acquired it, but some have found the code difficult to use. Furthermore, new members of the Lester group usually have to take considerable time learning all the options the code has to offer before they can use it successfully. In

  2. Quantum Monte Carlo Simulation of Vibrational Frequency Shifts of CO in Solid para-HYDROGEN

    NASA Astrophysics Data System (ADS)

    Wang, Lecheng; Le Roy, Robert; Roy, Pierre-Nicholas

    2014-06-01

    Stimulated by Fajardo's remarkable study of the rovibrational spectra of CO isotopologues trapped in solid para-hydrogen, we have performed quantum Monte Carlo simulations to predict his observed vibrational frequency shifts and inertial rotational constants using 2-body potentials based on the best available models for the pH_2-pH_2 and CO-pH_2, potential energy functions. We started by fitting an analytic `Morse/Long-Range' (MLR) function to the 1D ``adiabaic hindered rotor" version of Hinde's 5D pH_2-pH_2 potential developed by Faruk et al. We then modified it to take account of many-body effects by scaling it until it yielded the correct equilibrium lattice parameters for the fcc and hcp structures of pure solid para-hydrogen. A CO molecule was then placed at different interstitial or substitution sites in large equilibrated fcc or hcp para-hydrogen lattices, and the structural and dynamical behaviors of the micro-solvation environment around CO were simulated with a PIMC algorithm using a 2D effective pH_2-CO potential based on the 5D H_2--CO potential energy surface recently reported by Li et al., with a lattice sum of values of the 2D CO vibrational difference potential being use to predict the vibrational frequency shift. The effective rotational constants Beff for CO in different solid para-hydrogen structures were also calculated and compared with the experimental observations and with predicted Beff values for CO in large-sized para-hydrogen--CO clusters. M. E. Fajardo, J. Phys. Chem. A 117, 13504 (2013). R. Hinde, J. Chem. Phys., 128, 154308 (2008). H. Li, X-L. Zhang, R.J. Le Roy, and P.-N. Roy, J. Chem. Phys. 139, 164315 (2013). R.J. Le Roy, C.C. Haugen, J. Tao and Hui Li, Mol. Phys., 109, 435 (2011) N. Faruk, R.J. Le Roy, and P.-N. Roy, J. Chem. Phys. (submitted December 2013). Y. Mizumoto and Y. Ohtsuki, Chem. Phys. Lett. 501, 304 (2011).

  3. Bose-Einstein condensation in traps: A quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Dubois, Jonathan L.

    We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii (GP) equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N, and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [5, 6] up to liquid 4He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle "natural orbitals" and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation ( N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate "wave-function" and several other properties. We find that at low Boson density, na3 < 10-5 , where n = N/V and a is the hard core diameter, the GP theory of the condensate describes the whole system within 1%. At na3 ≈ 10-3 corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. Mean field theory fails at na3 ≳ 10-2. At high density, na 3 ≳ 0.1, the condensate is localized at the edges of the trap and, in

  4. Analysis of Quantum Monte Carlo Dynamics in Infinite-Range Ising Spin Systems:. Theory and its Possible Applications

    NASA Astrophysics Data System (ADS)

    Inoue, Jun-Ichi

    2013-09-01

    In terms of the stochastic process of a quantum-mechanical variant of Markov chain Monte Carlo method based on the Suzuki-Trotter decomposition, we analytically derive deterministic flows of order parameters such as magnetization in infinite-range (a mean-field like) quantum spin systems. Under the static approximation, differential equations with respect to order parameters are explicitly obtained from the Master equation that describes the microscopic-law in the corresponding classical system. We discuss several possible applications of our approach to several research topics, say, image processing and neural networks. This paper is written as a self-review of two papers1,2 for Symposium on Interface between Quantum Information and Statistical Physics at Kinki University in Osaka, Japan.

  5. Ab initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes

    NASA Astrophysics Data System (ADS)

    Groth, S.; Schoof, T.; Dornheim, T.; Bonitz, M.

    2016-02-01

    The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g., dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy. Recently, results for N =33 spin-polarized electrons at high density, rs=r ¯/aB≲4 , and low temperature have been obtained with the configuration path integral Monte Carlo (CPIMC) method [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015), 10.1103/PhysRevLett.115.130402]. To achieve these results, the original CPIMC algorithm [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011), 10.1002/ctpp.201100012] had to be further optimized to cope with the fermion sign problem (FSP). It is the purpose of this paper to give detailed information on the manifestation of the FSP in CPIMC simulations of the UEG and to demonstrate how it can be turned into a controllable convergence problem. In addition, we present new thermodynamic results for higher temperatures. Finally, to overcome the limitations of CPIMC towards strong coupling, we invoke an independent method—the recently developed permutation blocking path integral Monte Carlo approach [T. Dornheim et al., J. Chem. Phys. 143, 204101 (2015), 10.1063/1.4936145]. The combination of both approaches is able to yield ab initio data for the UEG over the entire density range, above a temperature of about one half of the Fermi temperature. Comparison with restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013), 10.1103/PhysRevLett.110.146405] allows us to quantify the systematic error arising from the free particle nodes.

  6. Electronic structure of solid FeO at high pressures by quantum Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Kolorenč, Jindřich; Mitas, Lubos

    2010-02-01

    We determine equation of state of stoichiometric FeO by employing the diffusion Monte Carlo method. The fermionic nodes of the many-body wave function are fixed by a single Slater determinant of one-particle orbitals extracted from spin-unrestricted Kohn-Sham equations utilizing a hybrid exchange-correlation functional. The calculated ambient pressure properties agree very well with available experimental data. At approximately 65 GPa, the atomic lattice is found to change from the rocksalt B1 to the NiAs-type inverse B8 structure.

  7. BCS-BEC crossover in two dimensions: A quantum Monte Carlo study

    SciTech Connect

    Bertaina, G.

    2012-09-26

    We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T= 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. We also consider the highly polarized gas and the competition between a polaronic and a molecular picture.

  8. Monte Carlo and quasi-Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Caflisch, Russel E.

    Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N-1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN-1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.

  9. Two- and Three-Nucleon Chiral Interactions in Quantum Monte Carlo Calculations for Nuclear Physics

    NASA Astrophysics Data System (ADS)

    Lynn, Joel; Carlson, Joseph; Gandolfi, Stefano; Gezerlis, Alexandros; Schmidt, Kevin; Schwenk, Achim; Tews, Ingo

    2015-10-01

    I present our recent work on Green's function Monte Carlo (GFMC) calculations of light nuclei using local two- and three-nucleon interactions derived from chiral effective field theory (EFT) up to next-to-next-to-leading order (N2LO). GFMC provides important benchmarking capabilities for other methods which rely on techniques to soften the nuclear interaction and also allows for nonperturbative studies of the convergence of the chiral EFT expansion. I discuss the choice of observables we make to fit the two low-energy constants which enter in the three-nucleon sector at N2LO: the 4He binding energy and n- α elastic scattering P-wave phase shifts. I then show some results for light nuclei. I also show our results for the energy per neutron in pure neutron matter using the auxiliary-field diffusion Monte Carlo method and discuss regulator choices. Finally I discuss some exciting future projects which are now possible. The NUCLEI SciDAC program and the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

  10. MCMini: Monte Carlo on GPGPU

    SciTech Connect

    Marcus, Ryan C.

    2012-07-25

    MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.

  11. Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties

    SciTech Connect

    Luo, Ye Sorella, Sandro; Zen, Andrea

    2014-11-21

    We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

  12. Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory.

    PubMed

    Ng, Yee-Hong; Bettens, Ryan P A

    2016-03-01

    Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations. PMID:26835785

  13. Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function.

    PubMed

    Rota, R; Casulleras, J; Mazzanti, F; Boronat, J

    2015-03-21

    We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function. PMID:25796238

  14. Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Humeniuk, Stephan

    2016-03-01

    Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers α of the interactions. The phase boundary for the ferromagnet is obtained as a function of α . For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization (M ,-M/2 ,-M/2 ) with unsaturated M <1 in a process known as "order by disorder" similar to the nearest-neighbor antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest-neighbor and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.

  15. Confinement transition of Z2 gauge theory coupled to fermions. A sign problem free quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Gazit, Snir; Randeria, Mohit; Vishwanath, Ashvin

    In two space dimensions, the Z2 lattice gauge theory is known to undergo a zero temperature confinement to de-confinment quantum phase transition . In this work, we study how this transition is modified in the presence of lattice fermions which are minimally coupled to the Z2 gauge field. This may be viewed as an extreme version of the BEC-BCS transition where fermions are confined in the strong coupling phase. We investigate both a square lattice model with a large fermi surface and Dirac fermions realized on a π flux and honeycomb lattices. The models are found to be free of the numerical sign problem for all fermion density. In addition, we introduce a numerical method to stochastically incorporate the Gauss law constraint in a quantum Monte Carlo (QMC) simulation. The phase diagram as a function of the model parameters, chemical potential and temperature is determined by means of a large scale determinant QMC.

  16. Statistical Exploration of Electronic Structure of Molecules from Quantum Monte-Carlo Simulations

    SciTech Connect

    Prabhat, Mr; Zubarev, Dmitry; Lester, Jr., William A.

    2010-12-22

    In this report, we present results from analysis of Quantum Monte Carlo (QMC) simulation data with the goal of determining internal structure of a 3N-dimensional phase space of an N-electron molecule. We are interested in mining the simulation data for patterns that might be indicative of the bond rearrangement as molecules change electronic states. We examined simulation output that tracks the positions of two coupled electrons in the singlet and triplet states of an H2 molecule. The electrons trace out a trajectory, which was analyzed with a number of statistical techniques. This project was intended to address the following scientific questions: (1) Do high-dimensional phase spaces characterizing electronic structure of molecules tend to cluster in any natural way? Do we see a change in clustering patterns as we explore different electronic states of the same molecule? (2) Since it is hard to understand the high-dimensional space of trajectories, can we project these trajectories to a lower dimensional subspace to gain a better understanding of patterns? (3) Do trajectories inherently lie in a lower-dimensional manifold? Can we recover that manifold? After extensive statistical analysis, we are now in a better position to respond to these questions. (1) We definitely see clustering patterns, and differences between the H2 and H2tri datasets. These are revealed by the pamk method in a fairly reliable manner and can potentially be used to distinguish bonded and non-bonded systems and get insight into the nature of bonding. (2) Projecting to a lower dimensional subspace ({approx}4-5) using PCA or Kernel PCA reveals interesting patterns in the distribution of scalar values, which can be related to the existing descriptors of electronic structure of molecules. Also, these results can be immediately used to develop robust tools for analysis of noisy data obtained during QMC simulations (3) All dimensionality reduction and estimation techniques that we tried seem to

  17. From hypernuclei to the Inner Core of Neutron Stars: A Quantum Monte Carlo Study

    NASA Astrophysics Data System (ADS)

    Lonardoni, D.; Pederiva, F.; Gandolfi, S.

    2014-08-01

    Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations have been employed to revise the interaction beween A-hyperons and nucleons in hypernuclei. The scheme used to describe the interaction, inspired by the phenomenological Argonne-Urbana forces, is the ΛN + ΛNN potential firstly introduced by Bodmer, Usmani et al. Within this framework, we performed calculations on light and medium mass hypernuclei in order to assess the extent of the repulsive contribution of the three-body part. By tuning this contribution in order to reproduce the Λ separation energy in 5ΛHe and 17ΛO, experimental findings are reproduced over a wide range of masses. Calculations have then been extended to Λ-neutron matter in order to derive an analogous of the symmetry energy to be used in determining the equation of state of matter in the typical conditions found in the inner core of neutron stars.

  18. Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

    NASA Astrophysics Data System (ADS)

    Deible, Michael J.; Kessler, Melody; Gasperich, Kevin E.; Jordan, Kenneth D.

    2015-08-01

    The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm-1, only slightly below the 935 cm-1 value derived from experiment.

  19. Parallelizing Monte Carlo with PMC

    SciTech Connect

    Rathkopf, J.A.; Jones, T.R.; Nessett, D.M.; Stanberry, L.C.

    1994-11-01

    PMC (Parallel Monte Carlo) is a system of generic interface routines that allows easy porting of Monte Carlo packages of large-scale physics simulation codes to Massively Parallel Processor (MPP) computers. By loading various versions of PMC, simulation code developers can configure their codes to run in several modes: serial, Monte Carlo runs on the same processor as the rest of the code; parallel, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on other MPP processor(s); distributed, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on a different machine. This multi-mode approach allows maintenance of a single simulation code source regardless of the target machine. PMC handles passing of messages between nodes on the MPP, passing of messages between a different machine and the MPP, distributing work between nodes, and providing independent, reproducible sequences of random numbers. Several production codes have been parallelized under the PMC system. Excellent parallel efficiency in both the distributed and parallel modes results if sufficient workload is available per processor. Experiences with a Monte Carlo photonics demonstration code and a Monte Carlo neutronics package are described.

  20. Wormhole Hamiltonian Monte Carlo

    PubMed Central

    Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak

    2015-01-01

    In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function. PMID:25861551

  1. A multi-agent quantum Monte Carlo model for charge transport: Application to organic field-effect transistors

    NASA Astrophysics Data System (ADS)

    Bauer, Thilo; Jäger, Christof M.; Jordan, Meredith J. T.; Clark, Timothy

    2015-07-01

    We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves.

  2. Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Qin, Mingpu; Shi, Hao; Zhang, Shiwei

    2016-08-01

    Ground-state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U /t from 2 to 8, for a range of densities including half-filling and n =0.3 ,0.5 ,0.6 ,0.75 , and 0.875 . At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasirandom sequences, which improves the convergence to the thermodynamic limit over pseudorandom and other sequences. With it and a careful finite size scaling analysis, we are able to obtain accurate values of ground-state properties in the thermodynamic limit. Detailed results for finite-sized systems up to 16 ×16 are also provided for benchmark purposes.

  3. Novel quantum Monte Carlo methods for spin-orbit Hamiltonians: 2D interacting electron gas with the Rashba interaction

    NASA Astrophysics Data System (ADS)

    Guo, Shi; Zhu, Minyi; Hu, Shuming; Mitas, Lubos

    2013-03-01

    Very recently, a quantum Monte Carlo (QMC) method was proposed for Rashba spin-orbit operators which expands the applicability of QMC to systems with variable spins. It is based on incorporating the spin-orbit into the Green's function and thus samples (ie, rotates) the spinors in the antisymmetric part of the trial function [1]. Here we propose a new alternative for both variational and diffusion Monte Carlo algorithms for calculations of systems with variable spins. Specifically, we introduce a new spin representation which allows us to sample the spin configurations efficiently and without introducing additional fluctuations. We develop the corresponding Green's function which treats the electron spin as a dynamical variable and we use the fixed-phase approximation to eliminate the negative probabilities. The trial wave function is a Slater determinant of spinors and spin-indepedent Jastrow correlations. The method also has the zero variance property. We benchmark the method on the 2D electron gas with the Rashba interaction and we find very good overall agreement with previously obtained results. Research supported by NSF and ARO.

  4. Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules

    NASA Astrophysics Data System (ADS)

    Suewattana, Malliga; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry; Walter, Eric J.

    2007-06-01

    The phaseless auxiliary-field quantum Monte Carlo (AF QMC) method [S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)] is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A-7A atoms and dimers: Al, Si, P, S, and Cl. In addition, the P2 dimer is compared to the third-row As2 dimer, which is also triply bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function ∣ΨT⟩ . As in previous calculations, a mean-field single Slater determinant is used as ∣ΨT⟩ . The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a plane wave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the plane wave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the plane wave method and discuss its convergence with respect to parameters such as the supercell size and plane wave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.

  5. A multi-agent quantum Monte Carlo model for charge transport: Application to organic field-effect transistors

    SciTech Connect

    Bauer, Thilo; Jäger, Christof M.; Jordan, Meredith J. T.; Clark, Timothy

    2015-07-28

    We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves.

  6. A multi-agent quantum Monte Carlo model for charge transport: Application to organic field-effect transistors.

    PubMed

    Bauer, Thilo; Jäger, Christof M; Jordan, Meredith J T; Clark, Timothy

    2015-07-28

    We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves. PMID:26233114

  7. Isotropic Monte Carlo Grain Growth

    2013-04-25

    IMCGG performs Monte Carlo simulations of normal grain growth in metals on a hexagonal grid in two dimensions with periodic boundary conditions. This may be performed with either an isotropic or a misorientation - and incliantion-dependent grain boundary energy.

  8. Toward Accurate Reaction Energetics for Molecular Line Growth at Surface: Quantum Monte Carlo and Density Functional Theory Calculations

    SciTech Connect

    Kanai, Y; Takeuchi, N

    2009-10-14

    We revisit the molecular line growth mechanism of styrene on the hydrogenated Si(001) 2x1 surface. In particular, we investigate the energetics of the radical chain reaction mechanism by means of diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) calculations. For the exchange correlation (XC) functional we use the non-empirical generalized-gradient approximation (GGA) and meta-GGA. We find that the QMC result also predicts the intra dimer-row growth of the molecular line over the inter dimer-row growth, supporting the conclusion based on DFT results. However, the absolute magnitudes of the adsorption and reaction energies, and the heights of the energy barriers differ considerably between the QMC and DFT with the GGA/meta-GGA XC functionals.

  9. Path-Integral Monte Carlo Study on a Droplet of a Dipolar Bose–Einstein Condensate Stabilized by Quantum Fluctuation

    NASA Astrophysics Data System (ADS)

    Saito, Hiroki

    2016-05-01

    Motivated by recent experiments [H. Kadau et al., Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.

  10. The roles of antiferromagnetic and nematic fluctuations in cuprate superconductors: a sign-free quantum Monte-Carlo study

    NASA Astrophysics Data System (ADS)

    Li, Zixiang; Yao, Hong; Wang, Fa; Lee, Dung-Hai

    Superconductivity is an emergent phenomena in the sense that the energy scale at which Cooper pairs form is generically much lower than the bare energy scale, namely the electron kinetic energy bandwidth. Addressing the mechanism of Cooper pairing amounts to finding out the effective interaction (or the renormalized interaction) that operates at the low energies. Finding such interaction from the bare microscopic Hamiltonian has not been possible for strong correlated superconductors such as the copper-oxide high temperature superconductor. In fact even one is given the effective interaction, determining its implied electronic instabilities without making any approximation has been a formidable task. Here, we perform sign-free quantum Monte-Carlo simulations to study the antiferromagnetic, superconducting, and the charge density wave instabilities which are ubiquitous in both electron and hole doped cuprates. Our result suggests only after including both the nematic and antiferromagnetic fluctuation, are the observed properties associated with these instabilities reproduced by the theory.

  11. Quantum Monte Carlo Calculation for the Equation of State of MgSiO3 perovskite at high pressures

    NASA Astrophysics Data System (ADS)

    Lin, Yangzheng; Cohen, R. E.; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim

    2014-03-01

    Magnesium silicate (MgSiO3) is among the most abundant minerals in the Earth's mantle. Its phase behavior under high pressure has important implications for the physical properties of deep Earth and the core-mantle boundary. A number of experiments and density functional theory calculations have studied perovskite and its transition to the post-perovskite phase. Here, we present our initial work on the equation of state of perovskite at pressures up to 200 GPa using quantum Monte Carlo (QMC), a benchmark ab initio method. Our QMC calculations optimize electron correlation by using a Slater-Jastrow type wave function with a single determinant comprised of single-particle orbitals extracted from fully converged DFT calculations. The equation of state obtained from QMC calculations agrees with experimental data. E-mail: rcohen@carnegiescience.edu; This work is supported by NSF.

  12. Binding and Diffusion of Lithium in Graphite: Quantum Monte Carlo Benchmarks and Validation of van der Waals Density Functional Methods

    SciTech Connect

    Ganesh, P.; Kim, Jeongnim; Park, Changwon; Yoon, Mina; Reboredo, Fernando A.; Kent, Paul R. C.

    2014-11-03

    In highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Moreover, the highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based on point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. Our results demonstrate that the lithium carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches.

  13. Binding and Diffusion of Lithium in Graphite: Quantum Monte Carlo Benchmarks and Validation of van der Waals Density Functional Methods.

    PubMed

    Ganesh, P; Kim, Jeongnim; Park, Changwon; Yoon, Mina; Reboredo, Fernando A; Kent, Paul R C

    2014-12-01

    Highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based on point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. The results demonstrate that the lithium-carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches. PMID:26583215

  14. Quantum Monte Carlo method for pairing phenomena: Supercounterfluid of two-species Bose gases in optical lattices

    SciTech Connect

    Ohgoe, Takahiro; Kawashima, Naoki

    2011-02-15

    We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by {ne}0,=0, and =0, where a and b are the order parameters of the two components, it is important to study behaviors of the pair-correlation function . For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.

  15. Quantum Monte Carlo method for pairing phenomena: Supercounterfluid of two-species Bose gases in optical lattices

    NASA Astrophysics Data System (ADS)

    Ohgoe, Takahiro; Kawashima, Naoki

    2011-02-01

    We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by ≠0,=0, and =0, where a and b are the order parameters of the two components, it is important to study behaviors of the pair-correlation function . For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.

  16. Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study

    NASA Astrophysics Data System (ADS)

    Pilati, S.; Zintchenko, I.; Troyer, M.

    2014-01-01

    Using continuous-space quantum Monte Carlo methods, we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and fully ferromagnetic phases. As the intensity of the optical lattice increases, the ferromagnetic instability takes place at weaker interactions, indicating a possible route to observe ferromagnetism in experiments performed with ultracold atoms. We compare our findings with previous predictions based on the standard computational method used in material science, namely density functional theory, and with results based on tight-binding models.

  17. Manager-worker-based model for the parallelization of Quantum Monte Carlo on heterogeneous and homogeneous networks.

    SciTech Connect

    Kent, David R., IV; Muller, Richard Partain; Cummings, Julian C.; Goddard, William A., III; Feldmann, Michael T.

    2007-10-01

    A manager-worker-based parallelization algorithm for Quantum Monte Carlo (QMC-MW) is presented and compared with the pure iterative parallelization algorithm, which is in common use. The new manager-worker algorithm performs automatic load balancing, allowing it to perform near the theoretical maximal speed even on heterogeneous parallel computers. Furthermore, the new algorithm performs as well as the pure iterative algorithm on homogeneous parallel computers. When combined with the dynamic distributable decorrelation algorithm (DDDA) [Feldmann et al., J Comput Chem 28, 2309 (2007)], the new manager-worker algorithm allows QMC calculations to be terminated at a prespecified level of convergence rather than upon a prespecified number of steps (the common practice). This allows a guaranteed level of precision at the least cost. Additionally, we show (by both analytic derivation and experimental verification) that standard QMC implementations are not perfectly parallel as is often claimed.

  18. Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

    SciTech Connect

    Deible, Michael J.; Kessler, Melody; Gasperich, Kevin E.; Jordan, Kenneth D.

    2015-08-28

    The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be{sub 2} is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be{sub 2} from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be{sub 2}, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm{sup −1}, only slightly below the 935 cm{sup −1} value derived from experiment.

  19. Systematic improvement of trial wavefunctions for Constrained Path Quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Clay, R. Torsten

    2007-03-01

    Constrained Path Monte Carlo (CPMC) provides an approximate solution to the Fermion sign problem for lattice models such as the Hubbard model. In the zero-temperature CPMC algorithm, a trial wavefunction is used to eliminate random walkers when their overlap with the trial function becomes zero. CPMC often produces surprisingly good results for ground state energy and correlation functions, even when a simple trial function is used. However, there is no reason to expect that simple wavefunctions (free electron or Hartree Fock) will have any overlap with complex correlated ground states. We therefore describe a method to improve CPMC results by optimizing the trial wavefunction. The trial function we use is a sum of Slater determinants that is optimized by the Path Integral Renormalization Group (PIRG) procedure. The wavefunction produced by PIRG is a sum of L determinants, with an energy that is variational. We show CPMC+PIRG data for a system where CPMC with a free electron trial function fails, the Hubbard model on an anisotropic triangular lattice.

  20. Quantum Monte Carlo calculation of the binding energy of the beryllium dimer.

    PubMed

    Deible, Michael J; Kessler, Melody; Gasperich, Kevin E; Jordan, Kenneth D

    2015-08-28

    The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm(-1), only slightly below the 935 cm(-1) value derived from experiment. PMID:26328827

  1. Magnetic ``three states of matter'' in two and three dimensions: a quantum Monte Carlo study of the extended toric codes

    NASA Astrophysics Data System (ADS)

    Kamiya, Yoshitomo

    The possibility of quantum spin liquids, characterized by nontrivial entanglement properties or a topological nonlocal order parameter, has long been debated both theoretically and experimentally. Since candidate systems (e.g., frustrated quantum magnets or 5 d transition metal oxides) may host other competing phases including conventional magnetic ordered phases, it is natural to ask what types of global phase diagrams can be anticipated depending on coupling constants, temperature, dimensionality, etc. In this talk, by considering an extension of the Kitaev toric code Hamiltonians by Ising interactions on 2D (square) and 3D (cubic) lattices, I will present thermodynamic phase diagrams featuring magnetic ``three states of matter,'' namely, quantum spin liquid, paramagnetic, and magnetically ordered phases (analogous to liquid, gas, and solid, respectively, in conventional matter) obtained by unbiased quantum Monte Carlo simulations [YK, Y. Kato, J. Nasu, and Y. Motome, PRB 92, 100403(R) (2015)]. We find that the ordered phase borders on the spin liquid around the exactly solvable point by a discontinuous transition line in 3D, while it grows continuously from the quantum critical point in 2D. In both cases, peculiar proximity effects to the nearby spin liquid phases are observed at high temperature even when the ground state is magnetically ordered. Such proximity effects include flux-shrinking and a tricritical behavior in 3D and a ``fractionalization'' of the order parameter field at the quantum critical point in 2D, both of which can be detected by measuring critical exponents. Work done in collaboration with Yasuyuki Kato, Joji Nasu, and Yukitoshi Motome.

  2. Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N.

    2016-08-01

    By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-1 /2 Heisenberg model with the first-neighbor (J1), second-neighbor (J2), and additional scalar chiral interaction JχSi.(Sj×Sk) on the triangular lattice. In the nonmagnetic phase of the J1-J2 triangular model with 0.08 ≲J2/J1≲0.16 , recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015), 10.1103/PhysRevB.92.041105 and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015), 10.1103/PhysRevB.92.140403] find a possible gapped spin liquid with the signal of a competition between a chiral and a Z2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction JχSi.(Sj×Sk) as a perturbation for this nonmagnetic phase. We find that with growing Jχ, the gapless U(1) Dirac spin liquid, which has the best variational energy for Jχ=0 , exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number C =1 /2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the J1-J2 triangular model.

  3. Static and Dynamical Correlation in Diradical Molecules by Quantum Monte Carlo Using the Jastrow Antisymmetrized Geminal Power Ansatz.

    PubMed

    Zen, Andrea; Coccia, Emanuele; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo

    2014-03-11

    Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃(3)B1-ã(1)A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC

  4. Quasi-Monte Carlo integration

    SciTech Connect

    Morokoff, W.J.; Caflisch, R.E.

    1995-12-01

    The standard Monte Carlo approach to evaluating multidimensional integrals using (pseudo)-random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement. As an alternative to the random methods, it has been suggested that lower error and improved convergence may be obtained by replacing the pseudo-random sequences with more uniformly distributed sequences known as quasi-random. In this paper quasi-random (Halton, Sobol`, and Faure) and pseudo-random sequences are compared in computational experiments designed to determine the effects on convergence of certain properties of the integrand, including variance, variation, smoothness, and dimension. The results show that variation, which plays an important role in the theoretical upper bound given by the Koksma-Hlawka inequality, does not affect convergence, while variance, the determining factor in random Monte Carlo, is shown to provide a rough upper bound, but does not accurately predict performance. In general, quasi-Monte Carlo methods are superior to random Monte Carlo, but the advantage may be slight, particularly in high dimensions or for integrands that are not smooth. For discontinuous integrands, we derive a bound which shows that the exponent for algebraic decay of the integration error from quasi-Monte Carlo is only slightly larger than {1/2} in high dimensions. 21 refs., 6 figs., 5 tabs.

  5. Quasi-Monte Carlo Integration

    NASA Astrophysics Data System (ADS)

    Morokoff, William J.; Caflisch, Russel E.

    1995-12-01

    The standard Monte Carlo approach to evaluating multidimensional integrals using (pseudo)-random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement. As an alternative to the random methods, it has been suggested that lower error and improved convergence may be obtained by replacing the pseudo-random sequences with more uniformly distributed sequences known as quasi-random. In this paper quasi-random (Halton, Sobol', and Faure) and pseudo-random sequences are compared in computational experiments designed to determine the effects on convergence of certain properties of the integrand, including variance, variation, smoothness, and dimension. The results show that variation, which plays an important role in the theoretical upper bound given by the Koksma-Hlawka inequality, does not affect convergence, while variance, the determining factor in random Monte Carlo, is shown to provide a rough upper bound, but does not accurately predict performance. In general, quasi-Monte Carlo methods are superior to random Monte Carlo, but the advantage may be slight, particularly in high dimensions or for integrands that are not smooth. For discontinuous integrands, we derive a bound which shows that the exponent for algebraic decay of the integration error from quasi-Monte Carlo is only slightly larger than {1}/{2} in high dimensions.

  6. Quantum Monte Carlo calculations of structural and electronic properties in the correlated oxide NiO

    NASA Astrophysics Data System (ADS)

    Mitra, Chandrima; Krogel, Jaron; Santana Palacio, Juan A.; Reboredo, Fernando A.

    2015-03-01

    Transition metal oxides pose difficulties for condensed matter theories due to the presence of strong electronic correlations. The complex interplay among correlation and exchange in d subshells, crystal field effects, p-d hybridization and charge transfer gives rise to a rich variety of structural and electronic phases. NiO is one such challenging d system, where conventional band theory fails. Compared to the experimental value, the cohesive energy of bulk NiO computed within DFT-LDA differs by almost a factor of 18 %. Band gap computed within standard local or semi-local functionals are off by a factor of 80 %. A quasi-particle correction like the G0W0 approach cannot correct the band gap and is still by far too low. In this work we adopt the Diffusion Quantum Monte (DMC) approach to study the structural and electronic properties of NiO. Trial wave-functions were self consistently generated in a Slater-Jastrow form. To test pseudopotentials used, DMC calculations were done on atomic Ni and O and their computed ionization potentials showed excellent agreement with experiments (within 0.04%). The equilibrium bond length and binding energy of the NiO dimer were also computed that were 0.001% and 0.03%, respectively, from experimental values. DMC calculations of equation of state and band gap of bulk NiO will be presented. We gratefully acknowledge support from U.S Department of Energy, Basic Energy Sciences, Materials Science and Engineering Division.

  7. Monte Carlo studies of the self-correcting properties of the Majorana quantum error correction code under braiding

    NASA Astrophysics Data System (ADS)

    Pedrocchi, Fabio L.; Bonesteel, N. E.; DiVincenzo, David P.

    2015-09-01

    The Majorana code is an example of a stabilizer code where the quantum information is stored in a system supporting well-separated Majorana bound states (MBSs). We focus on one-dimensional realizations of the Majorana code, as well as networks of such structures, and investigate their lifetime when coupled to a parity-preserving thermal environment. We apply the Davies prescription, a standard method that describes the basic aspects of a thermal environment, and derive a master equation in the Born-Markov limit. We first focus on a single wire with immobile MBSs and perform error correction to annihilate thermal excitations. In the high-temperature limit, we show both analytically and numerically that the lifetime of the Majorana qubit grows logarithmically with the size of the wire. We then study a trijunction with four MBSs when braiding is executed. We study the occurrence of dangerous error processes that prevent the lifetime of the Majorana code from growing with the size of the trijunction. The origin of the dangerous processes is the braiding itself, which separates pairs of excitations and renders the noise nonlocal; these processes arise from the basic constraints of moving MBSs in one-dimensional (1D) structures. We confirm our predictions with Monte Carlo simulations in the low-temperature regime, i.e., the regime of practical relevance. Our results put a restriction on the degree of self-correction of this particular 1D topological quantum computing architecture.

  8. Characterization and Monte Carlo simulation of single ion Geiger mode avalanche diodes integrated with a quantum dot nanostructure

    NASA Astrophysics Data System (ADS)

    Sharma, Peter; Abraham, J. B. S.; Ten Eyck, G.; Childs, K. D.; Bielejec, E.; Carroll, M. S.

    Detection of single ion implantation within a nanostructure is necessary for the high yield fabrication of implanted donor-based quantum computing architectures. Single ion Geiger mode avalanche (SIGMA) diodes with a laterally integrated nanostructure capable of forming a quantum dot were fabricated and characterized using photon pulses. The detection efficiency of this design was measured as a function of wavelength, lateral position, and for varying delay times between the photon pulse and the overbias detection window. Monte Carlo simulations based only on the random diffusion of photo-generated carriers and the geometrical placement of the avalanche region agrees qualitatively with device characterization. Based on these results, SIGMA detection efficiency appears to be determined solely by the diffusion of photo-generated electron-hole pairs into a buried avalanche region. Device performance is then highly dependent on the uniformity of the underlying silicon substrate and the proximity of photo-generated carriers to the silicon-silicon dioxide interface, which are the most important limiting factors for reaching the single ion detection limit with SIGMA detectors. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.

  9. Proton Upset Monte Carlo Simulation

    NASA Technical Reports Server (NTRS)

    O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.

    2009-01-01

    The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.

  10. Reaction pathways by quantum Monte Carlo: Insight on the torsion barrier of 1,3-butadiene, and the conrotatory ring opening of cyclobutene

    NASA Astrophysics Data System (ADS)

    Barborini, Matteo; Guidoni, Leonardo

    2012-12-01

    Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011), 10.1021/jp2051596]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.

  11. Monte Carlo calculations of nuclei

    SciTech Connect

    Pieper, S.C.

    1997-10-01

    Nuclear many-body calculations have the complication of strong spin- and isospin-dependent potentials. In these lectures the author discusses the variational and Green`s function Monte Carlo techniques that have been developed to address this complication, and presents a few results.

  12. Multilevel sequential Monte Carlo samplers

    DOE PAGESBeta

    Beskos, Alexandros; Jasra, Ajay; Law, Kody; Tempone, Raul; Zhou, Yan

    2016-08-24

    Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levelsmore » $${\\infty}$$ >h0>h1 ...>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.« less

  13. Synchronous Parallel Kinetic Monte Carlo

    SciTech Connect

    Mart?nez, E; Marian, J; Kalos, M H

    2006-12-14

    A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm provides an exact generalization of any standard serial kMC model and is trivially implemented in parallel architectures. We demonstrate the mathematical validity and parallel performance of the method by solving several well-understood problems in diffusion.

  14. Competing collinear magnetic structures in superconducting FeSe by first-principles quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Busemeyer, Brian; Dagrada, Mario; Sorella, Sandro; Casula, Michele; Wagner, Lucas K.

    2016-07-01

    Resolving the interplay between magnetic interactions and structural properties in strongly correlated materials through a quantitatively accurate approach has been a major challenge in condensed-matter physics. Here we apply highly accurate first-principles quantum Monte Carlo (QMC) techniques to obtain structural and magnetic properties of the iron selenide (FeSe) superconductor under pressure. Where comparable, the computed properties are very close to the experimental values. Of potential ordered magnetic configurations, collinear spin configurations are the most energetically favorable over the explored pressure range. They become nearly degenerate in energy with bicollinear spin orderings at around 7 GPa, when the experimental critical temperature Tc is the highest. On the other hand, ferromagnetic, checkerboard, and staggered dimer configurations become relatively higher in energy as the pressure increases. The behavior under pressure is explained by an analysis of the local charge compressibility and the orbital occupation as described by the QMC many-body wave function, which reveals how spin, charge, and orbital degrees of freedom are strongly coupled in this compound. This remarkable pressure evolution suggests that stripelike magnetic fluctuations may be responsible for the enhanced Tc in FeSe and that higher Tc is associated with nearness to a crossover between collinear and bicollinear ordering.

  15. Cohesive energy and structural parameters of binary oxides of groups IIA and IIIB from diffusion quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.; Reboredo, Fernando A.

    2016-05-01

    We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.

  16. The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

    NASA Astrophysics Data System (ADS)

    Viel, Alexandra; Coutinho-Neto, Maurício D.; Manthe, Uwe

    2007-01-01

    Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7±0.3cm-1 is obtained, and the vibrational ground state energy is found to be 15122±4cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21±0.09cm-1 and the vibrational ground state energy to 14385±2cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

  17. The ground state tunneling splitting and the zero point energy of malonaldehyde: a quantum Monte Carlo determination.

    PubMed

    Viel, Alexandra; Coutinho-Neto, Maurício D; Manthe, Uwe

    2007-01-14

    Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface. PMID:17228955

  18. Improved measurement scheme of the self energy in the worm-sampled hybridization-expansion quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Han, Mancheon; Lee, Choong-Ki; Choi, Hyoung Joon

    Hybridization-expansion continuous-time quantum Monte Carlo (CT-HYB) is a popular approach in real material researches because it allows to deal with non-density-density-type interaction. In the conventional CT-HYB, we measure Green's function and find the self energy from the Dyson equation. Because one needs to compute the inverse of the statistical data in this approach, obtained self energy is very sensitive to statistical noise. For that reason, the measurement is not reliable except for low frequencies. Such an error can be suppressed by measuring a special type of higher-order correlation function and is implemented for density-density-type interaction. With the help of the recently reported worm-sampling measurement, we developed an improved self energy measurement scheme which can be applied to any type of interactions. As an illustration, we calculated the self energy for the 3-orbital Hubbard-Kanamori-type Hamiltonian with our newly developed method. This work was supported by NRF of Korea (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2015-C3-039)

  19. Many-body ab initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO

    SciTech Connect

    Mitra, Chandrima; Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A.

    2015-10-28

    We present a many-body diffusion quantum Monte Carlo (DMC) study of the bulk and defect properties of NiO. We find excellent agreement with experimental values, within 0.3%, 0.6%, and 3.5% for the lattice constant, cohesive energy, and bulk modulus, respectively. The quasiparticle bandgap was also computed, and the DMC result of 4.72 (0.17) eV compares well with the experimental value of 4.3 eV. Furthermore, DMC calculations of excited states at the L, Z, and the gamma point of the Brillouin zone reveal a flat upper valence band for NiO, in good agreement with Angle Resolved Photoemission Spectroscopy results. To study defect properties, we evaluated the formation energies of the neutral and charged vacancies of oxygen and nickel in NiO. A formation energy of 7.2 (0.15) eV was found for the oxygen vacancy under oxygen rich conditions. For the Ni vacancy, we obtained a formation energy of 3.2 (0.15) eV under Ni rich conditions. These results confirm that NiO occurs as a p-type material with the dominant intrinsic vacancy defect being Ni vacancy.

  20. Global phase diagram of the stacked frustrated triangular Ising system in a transverse field: a quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Ma, Han; Lou, Jie; Tsvelik, Alexei; Kawashima, Naoki; Chen, Yan

    2014-03-01

    The global phase diagram of the stacked frustrated triangular Ising magnet in a transverse field is obtained by using continuous time quantum Monte Carlo method. As the inter-plane interaction is strengthened, an first-order transition from a ferrimagnetic phase with two equivalent sublattices (FR2) to a partially disordered antiferrimagnetic phase (AF) occurs at small transverse field. In the quasi-one dimensional case, i.e. antiferromagnetically coupled transverse Ising chains, which corresponds to the realistic material CoNb2O6, our simulation reveals the existence of the low-field FR2 phase. In contrast, in the quasi-two dimensional limit, i.e. weakly coupled triangular Ising magnet, upon increasing the transverse magnetic field, the FR2 and AF phases successively appear in the order. In the vicinity of the ordered-disordered phase transition, the nature of phases can hardly be identified within our computational ability. At large transverse field, the paramagnetic phase trivially appears. Future experiments on CoNb2O6 at low temperature are expected to evidence the different magnetic patterns of this frustrated magnet based on our results in the quasi-one dimensional limit.

  1. Quantum Monte Carlo simulation of antiferromagnetic spin ladder (C5H12N)2CuBr4

    NASA Astrophysics Data System (ADS)

    Freitas, Augusto S.

    2016-07-01

    In this paper I present a Quantum Monte Carlo (QMC) study of the magnetic properties of an antiferromagnetic spin ladder (C5H12N)2CuBr4. This compound is the prototype of the Heisenberg model for a two leg spin ladder in the presence of an external magnetic field. The susceptibility phase diagram has a rounded peak in the vicinity of T=7.4 K, obeys Troyer's law for low temperatures, and Curie's law for high temperatures. I also study the susceptibility diagram in low temperatures and I found the spin gap Δ=9.26 K, in good concordance with the experimental value, 9.5 K. In high field, I present a diagram of magnetization as a function of temperature. In the vicinity of a critical field, Hci, the magnetization scales with T1/2 and this result was found also in the QMC simulation. In all the results, there is a very good concordance with the experimental data. I also show in this paper that the spin gap is null and the susceptibility is proportional to T for low temperatures when relatively high values of the ladders' coupling is taken in account.

  2. Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations.

    PubMed

    Gillan, M J; Alfè, D; Manby, F R

    2015-09-14

    The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values. PMID:26374005

  3. Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: The Ti4O7 Magneli phase

    DOE PAGESBeta

    Benali, Anouar; Shulenburger, Luke; Krogel, Jaron T.; Zhong, Xiaoling; Kent, Paul R. C.; Heinonen, Olle

    2016-06-07

    The Magneli phase Ti4O7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low- lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate Quantum Monte Carlo methods. We compare our results to those obtained from density functional theory- based methods that include approximate corrections for exchange and correlation. Our resultsmore » confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. Here, a detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.« less

  4. Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function

    NASA Astrophysics Data System (ADS)

    Shepherd, James J.; Scuseria, Gustavo E.; Spencer, James S.

    2014-10-01

    We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schrödinger equation with substantially reduced computational cost compared with exact diagonalization. We find k -space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of 1038 determinants) in 250 core hours, substantially quicker than the ˜1036 core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.

  5. Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Booth, George H.; Cleland, Deidre; Thom, Alex J. W.; Alavi, Ali

    2011-08-01

    The full configuration interaction quantum Monte Carlo (FCIQMC) method, as well as its "initiator" extension (i-FCIQMC), is used to tackle the complex electronic structure of the carbon dimer across the entire dissociation reaction coordinate, as a prototypical example of a strongly correlated molecular system. Various basis sets of increasing size up to the large cc-pVQZ are used, spanning a fully accessible N-electron basis of over 1012 Slater determinants, and the accuracy of the method is demonstrated in each basis set. Convergence to the FCI limit is achieved in the largest basis with only O[10^7] walkers within random errorbars of a few tenths of a millihartree across the binding curve, and extensive comparisons to FCI, CCSD(T), MRCI, and CEEIS results are made where possible. A detailed exposition of the convergence properties of the FCIQMC methods is provided, considering convergence with elapsed imaginary time, number of walkers and size of the basis. Various symmetries which can be incorporated into the stochastic dynamic, beyond the standard abelian point group symmetry and spin polarisation are also described. These can have significant benefit to the computational effort of the calculations, as well as the ability to converge to various excited states. The results presented demonstrate a new benchmark accuracy in basis-set energies for systems of this size, significantly improving on previous state of the art estimates.

  6. Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: the Ti4O7 Magnéli phase.

    PubMed

    Benali, Anouar; Shulenburger, Luke; Krogel, Jaron T; Zhong, Xiaoliang; Kent, Paul R C; Heinonen, Olle

    2016-07-21

    The Magnéli phase Ti4O7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low-lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate quantum Monte Carlo methods. We compare our results to those obtained from density functional theory-based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. A detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps. PMID:27334262

  7. Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations

    SciTech Connect

    Gillan, M. J.; Alfè, D.; Manby, F. R.

    2015-09-14

    The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH{sub 4}-H{sub 2}O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.

  8. Cohesive energy and structural parameters of binary oxides of groups IIA and IIIB from diffusion quantum Monte Carlo.

    PubMed

    Santana, Juan A; Krogel, Jaron T; Kent, Paul R C; Reboredo, Fernando A

    2016-05-01

    We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc2O3, Y2O3, and La2O3. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides. PMID:27155647

  9. Phase Boundary between MgSiO3 Perovskite and Post-perovskite from Quantum Monte Carlo Simulations

    NASA Astrophysics Data System (ADS)

    Lin, Yangzheng; Cohen, R. E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim

    2015-03-01

    Accurate prediction of the phase boundary between perovskite (pv) and post-perovskite (ppv) phases of MgSiO3 is important to explain many unusual properties of the Earth's D'' layer, such as lateral variations in the depth of the observed seismic discontinuity and seismic anisotropy. We have performed quantum Monte Carlo (QMC) simulations with the QMCPACK code on GPU clusters to obtain the ground state equation of state. Density functional perturbation theory (DFPT) computations were performed to obtain the thermal pressure within quasiharmonic lattice dynamics. The equations of state for both phases of MgSiO3 and their phase boundary from our QMC simulations agree well with experiment results and better than previous DFT calculations. Double-crossing of the pv-ppv boundary along Earth's geotherm depends on the effects of iron on the transition. Computations were performed on XSEDE machine Stampede, and on the Oak Ridge Leadership Computing Facility (OLCF) machine Titan from INCITE program. This work is supported by NSF.

  10. Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

    NASA Astrophysics Data System (ADS)

    Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.

    2014-04-01

    Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.

  11. Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

    SciTech Connect

    Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E

    2014-01-01

    Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.

  12. Binding and Diffusion of Lithium in Graphite: Quantum Monte Carlo Benchmarks and Validation of van der Waals Density Functional Methods

    DOE PAGESBeta

    Ganesh, P.; Kim, Jeongnim; Park, Changwon; Yoon, Mina; Reboredo, Fernando A.; Kent, Paul R. C.

    2014-11-03

    In highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Moreover, the highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based onmore » point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. Our results demonstrate that the lithium carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches.« less

  13. Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements.

    PubMed

    Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei

    2006-10-21

    A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson et al. [J. Chem. Phys. 119, 11099 (2003); 119, 11113 (2003)], which employ a small-core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density functional (generalized gradient approximation and B3LYP) and CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few millihartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment. PMID:17059242

  14. Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo

    SciTech Connect

    Wendland, D.; Ballenegger, V.; Alastuey, A.

    2014-11-14

    We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

  15. Monte Carlo Simulation for Perusal and Practice.

    ERIC Educational Resources Information Center

    Brooks, Gordon P.; Barcikowski, Robert S.; Robey, Randall R.

    The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…

  16. Monte Carlo Simulation of Quantum Transport in Semiconductors Using Wigner Paths

    NASA Astrophysics Data System (ADS)

    Bertoni, A.; García-García, J.; Bordone, P.; Brunetti, R.; Jacoboni, C.

    Charge transport in mesoscopic semiconductor systems must be analyzed in terms of a quantum theory since nowadays typical dimensions of the physical structures are comparable with the electron coherence length. Theoretical approaches based on fully quantum mechanical grounds have been developed in the last decade with the purpose of analyzing the quantum electron-phonon interaction in electron transport. The Wigner function (WF) formalism is particularly suitable for the analysis of mesoscopic structures owing to its phase-space formulation that allows a natural treatment of space dependent problems with given boundary conditions. The Hamiltonian describing the system is [1] {H}=-frac{hbar^2}{2m}nabla^2 +sum_qb... ...iqr} ) +V(r) +eE\\cdot r

  17. Monte Carlo methods in ICF

    SciTech Connect

    Zimmerman, G.B.

    1997-06-24

    Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ion and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved 50X in efficiency by angular biasing the x-rays towards the fuel capsule. Accurate simulation of thermonuclear burns nd burn diagnostics involves detailed particle source spectra, charged particle ranges, inflight reaction kinematics, corrections for bulk and thermal Doppler effects and variance reduction to obtain adequate statistics for rare events. It is found that the effects of angular Coulomb scattering must be included in models of charged particle transport through heterogeneous materials.

  18. The D0 Monte Carlo

    SciTech Connect

    Womersley, J. . Dept. of Physics)

    1992-10-01

    The D0 detector at the Fermilab Tevatron began its first data taking run in May 1992. For analysis of the expected 25 pb[sup [minus]1] data sample, roughly half a million simulated events will be needed. The GEANT-based Monte Carlo program used to generate these events is described, together with comparisons to test beam data. Some novel techniques used to speed up execution and simplify geometrical input are described.

  19. Extending canonical Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Velazquez, L.; Curilef, S.

    2010-02-01

    In this paper, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation for the extension of the available Monte Carlo methods on the basis of the consideration of the Gibbs canonical ensemble to account for the existence of an anomalous regime with negative heat capacities C < 0. The resulting framework appears to be a suitable generalization of the methodology associated with the so-called dynamical ensemble, which is applied to the extension of two well-known Monte Carlo methods: the Metropolis importance sampling and the Swendsen-Wang cluster algorithm. These Monte Carlo algorithms are employed to study the anomalous thermodynamic behavior of the Potts models with many spin states q defined on a d-dimensional hypercubic lattice with periodic boundary conditions, which successfully reduce the exponential divergence of the decorrelation time τ with increase of the system size N to a weak power-law divergence \\tau \\propto N^{\\alpha } with α≈0.2 for the particular case of the 2D ten-state Potts model.

  20. Compressible generalized hybrid Monte Carlo

    NASA Astrophysics Data System (ADS)

    Fang, Youhan; Sanz-Serna, J. M.; Skeel, Robert D.

    2014-05-01

    One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods typically inch through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in principle by embedding configuration space in a higher dimensional phase space and using ordinary differential equations. In practice, numerical integrators must be used, lowering the acceptance rate. This is the essence of hybrid Monte Carlo methods. Presented is a general framework for constructing such methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed. The possibilities are illustrated by deriving a couple of explicit hybrid Monte Carlo methods, one based on barrier-lowering variable-metric dynamics and another based on isokinetic dynamics.

  1. Metallic behavior in two dimensional interacting electron systems in the presence of disorder: Quantum Monte-Carlo Studies

    NASA Astrophysics Data System (ADS)

    Scalettar, Richard

    2004-03-01

    We study the temperature and (Zeeman) magnetic field-dependent conductivity σ(B,T) of the two-dimensional disordered Hubbard model. In the absence of a field, calculations of the current-current correlation function using the Determinant Quantum Monte Carlo method show that repulsion between electrons can significantly enhance the conductivity, and, at temperatures in the same range as those of experiments (about 0.1 E_f), change the sign of dσ/dT from positive (insulating behavior) to negative (conducting behavior). This result suggests the possibility of a metallic phase, and consequently a metal--insulator transition, in a two-dimensional microscopic model containing both interactions and disorder. A Zeeman magnetic field suppresses the metallic behavior and is able to induce a metal--insulator transition at a critical field strength. We argue that the qualitative features of this magnetoconductance are in agreement with experimental findings in two-dimensional electron- and hole-gases in semiconductor structures. Finally, we discuss the role of particle-hole symmetry in determining the effects of disorder on the transport and thermodynamic properties. This work was supported by NSF-DMR-0312261. ``Conducting phase in the two-dimensional disordered Hubbard model,'' P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, Phys. Rev. Lett. 83, 4610 (1999). ``Particle-Hole Symmetry and the Effect of Disorder on the Mott--Hubbard Insulator,'' P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, Phys. Rev. Lett. 87, 146401 (2001). ``Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field,'' P.J.H. Denteneer and R.T. Scalettar, Phys. Rev. Lett. 90, 246401 (2003).

  2. Path Integral Monte Carlo Methods for Fermions

    NASA Astrophysics Data System (ADS)

    Ethan, Ethan; Dubois, Jonathan; Ceperley, David

    2014-03-01

    In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.

  3. Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

    NASA Astrophysics Data System (ADS)

    Härtle, R.; Cohen, G.; Reichman, D. R.; Millis, A. J.

    2015-08-01

    We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort. We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the nonmonotonic temperature dependence of the steady-state magnetization as a result of competing broadening effects. We also elucidate the pronounced nonlinear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.

  4. Monte Carlo methods and applications in nuclear physics

    SciTech Connect

    Carlson, J.

    1990-01-01

    Monte Carlo methods for studying few- and many-body quantum systems are introduced, with special emphasis given to their applications in nuclear physics. Variational and Green's function Monte Carlo methods are presented in some detail. The status of calculations of light nuclei is reviewed, including discussions of the three-nucleon-interaction, charge and magnetic form factors, the coulomb sum rule, and studies of low-energy radiative transitions. 58 refs., 12 figs.

  5. Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule

    NASA Astrophysics Data System (ADS)

    Caffarel, Michel; Applencourt, Thomas; Giner, Emmanuel; Scemama, Anthony

    2016-04-01

    All-electron Fixed-node Diffusion Monte Carlo calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a selected Configuration Interaction calculation [Configuration Interaction using a Perturbative Selection done Iteratively (CIPSI) method] including up to about 1.4 × 106 of determinants. Calculations are made using the cc-pCVnZ family of basis sets, with n = 2 to 5. In contrast with most quantum Monte Carlo works no re-optimization of the determinantal part in presence of a Jastrow is performed. For the largest cc-pCV5Z basis set the lowest upper bound for the ground-state energy reported so far of -76.437 44(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal number n and the Complete Basis Set limit associated with exact nodes is easily extracted. The resulting energy of -76.438 94(12) — in perfect agreement with the best experimentally derived value — is the most accurate theoretical estimate reported so far. We emphasize that employing selected configuration interaction nodes of increasing quality in a given family of basis sets may represent a simple, deterministic, reproducible, and systematic way of controlling the fixed-node error in diffusion Monte Carlo.

  6. Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule

    PubMed Central

    Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo

    2014-01-01

    Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets. PMID:24526929

  7. Self-healing diffusion quantum Monte Carlo algorithms: Direct reduction of the fermion sign error in electronic structure calculations

    NASA Astrophysics Data System (ADS)

    Reboredo, F. A.; Hood, R. Q.; Kent, P. R. C.

    2009-05-01

    We develop a formalism and present an algorithm for optimization of the trial wave function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground-state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project out a multideterminant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multideterminant expansions of the trial wave function. The method can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where benchmark configuration-interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal noninteracting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77, 245110 (2008)]. Tests of the method are extended to a

  8. Multidimensional stochastic approximation Monte Carlo.

    PubMed

    Zablotskiy, Sergey V; Ivanov, Victor A; Paul, Wolfgang

    2016-06-01

    Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}). PMID:27415383

  9. Monte Carlo surface flux tallies

    SciTech Connect

    Favorite, Jeffrey A

    2010-11-19

    Particle fluxes on surfaces are difficult to calculate with Monte Carlo codes because the score requires a division by the surface-crossing angle cosine, and grazing angles lead to inaccuracies. We revisit the standard practice of dividing by half of a cosine 'cutoff' for particles whose surface-crossing cosines are below the cutoff. The theory behind this approximation is sound, but the application of the theory to all possible situations does not account for two implicit assumptions: (1) the grazing band must be symmetric about 0, and (2) a single linear expansion for the angular flux must be applied in the entire grazing band. These assumptions are violated in common circumstances; for example, for separate in-going and out-going flux tallies on internal surfaces, and for out-going flux tallies on external surfaces. In some situations, dividing by two-thirds of the cosine cutoff is more appropriate. If users were able to control both the cosine cutoff and the substitute value, they could use these parameters to make accurate surface flux tallies. The procedure is demonstrated in a test problem in which Monte Carlo surface fluxes in cosine bins are converted to angular fluxes and compared with the results of a discrete ordinates calculation.

  10. Multidimensional stochastic approximation Monte Carlo

    NASA Astrophysics Data System (ADS)

    Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang

    2016-06-01

    Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .

  11. 1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO

    SciTech Connect

    T. EVANS; ET AL

    2000-08-01

    We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.

  12. Dynamic Cluster Quantum Monte Carlo Simulations of a Two-Dimensional Hubbard Model with Stripelike Charge-Density-Wave Modulations: Interplay between Inhomogeneities and the Superconducting State

    SciTech Connect

    Maier, Thomas A; Alvarez, Gonzalo; Summers, Michael Stuart; Schulthess, Thomas C

    2010-01-01

    Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1=8 doped two-dimensional Hubbard model with imposed unidirectional stripelike charge-density-wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for a moderate modulation strength due to a delicate balance between the modulation enhanced pairing interaction, and a concomitant suppression of the bare particle-particle excitations by a modulation reduction of the quasiparticle weight.

  13. Positron and positronium chemistry by quantum Monte Carlo. V. The ground state potential energy curve of e+LiH

    NASA Astrophysics Data System (ADS)

    Mella, Massimo; Morosi, Gabriele; Bressanini, Dario; Elli, Stefano

    2000-10-01

    The potential energy curve of e+LiH has been computed by means of diffusion Monte Carlo using explicitly correlated trial wave functions. This curve allows us to compute the adiabatic total and binding energies and the vibrational spectrum of e+LiH, and the adiabatic positron affinity of LiH. Using these results, we discuss the possibility to detect spectroscopically e+LiH in the gas phase, in order to have the first direct observation of a positron-containing system.

  14. Instantons and scaling of the transitions rates in Quantum Monte Carlo simulations of thermally-assisted quantum tunneling in spin systems

    NASA Astrophysics Data System (ADS)

    Smelyanskiy, Vadim; Jiang, Zhang; Boixo, Sergio; Issakov, Sergei; Mazzola, Guglielmo; Troyer, Matthias; Neven, Hartmut

    We study analytically and numerically the dynamics of the quantum Monte Carlo (QMC) algorithm to simulate thermally-assisted tunneling in mean-field spin models without conservation of total spin. We use Kramers escape rate theory to calculate the scaling of the QMC time with the problem size to simulate the tunneling transitions. We develop path-integral instanton approach in coherent state and Suzuki-Trotter representations to calculate the escape rate and most probable escape path in QMC dynamics. Analtytical results are in a good agreement with numerical studies. We identify the class of models where the exponent in the scaling of the QMC time is the same as that in physical tunneling but the pre-factor depends very significantly on the QMC path representation. We propose the classes of problems where QMC can fail to simulate tunneling efficiently. The work of GM and MT has been supported by the Swiss National Science Foundation through the National Competence Center in Research QSIT and by ODNI, IARPA via MIT Lincoln Laboratory Air Force Contract No. FA8721-05-C-0002.

  15. Quantum Monte Carlo calculations of magnetic moments and M1 transitions in A{<=}7 nuclei including meson-exchange currents

    SciTech Connect

    Marcucci, L. E.; Pervin, Muslema; Pieper, Steven C.; Wiringa, R. B.; Schiavilla, R.

    2008-12-15

    Green's function Monte Carlo calculations of magnetic moments and M1 transitions including two-body meson-exchange current (MEC) contributions are reported for A{<=}7 nuclei. The realistic Argonne v{sub 18} two-nucleon and Illinois-2 three-nucleon potentials are used to generate the nuclear wave functions. The two-body meson-exchange operators are constructed to satisfy the continuity equation with the Argonne v{sub 18} potential. The MEC contributions increase the A=3,7 isovector magnetic moments by 16% and the A=6,7 M1 transition rates by 17-34%, bringing them into very good agreement with the experimental data.

  16. Quantum Monte Carlo for the x-ray absorption spectrum of pyrrole at the nitrogen K-edge

    SciTech Connect

    Zubarev, Dmitry Yu.; Austin, Brian M.; Lester, William A. Jr.

    2012-04-14

    Fixed-node diffusion Monte Carlo (FNDMC) is used to simulate the x-ray absorption spectrum of a gas-phase pyrrole molecule at the nitrogen K-edge. Trial wave functions for core-excited states are constructed from ground-state Kohn-Sham determinants substituted with singly occupied natural orbitals from configuration interaction with single excitations calculations of the five lowest valence-excited triplet states. The FNDMC ionization potential (IP) is found to lie within 0.3 eV of the experimental value of 406.1 {+-} 0.1 eV. The transition energies to anti-bonding virtual orbitals match the experimental spectrum after alignment of IP values and agree with the existing assignments.

  17. Electronic states of Al and Al{sub 2} using quantum Monte Carlo with an effective core potential

    SciTech Connect

    Greeff, C.W.; Lester, W.A. Jr.; Hammond, B.L.

    1996-02-01

    The diffusion Monte Carlo method is applied in conjunction with an ab initio effective core potential to compute energies of some neutral and charged states of Al and Al{sub 2}. The computed ionization potentials, electron affinities and dissociation energies differ from measured values by at most a few hundredths of eV. The computed dissociation energy of Al{sub 2} agrees with the most extensive CI calculations. It appears that our dissociation energy for Al{sup {minus}}{sub 2} is the most accurate to date. The quality of the results indicates that the use of the pseudopotential is not an important limitation on the accuracy of these calculations. Variational wavefunctions with Boys-Handy correlation functions are found to give more than 70{percent} of the correlation energy with 8 optimized parameters. These optimized trial functions are used together with numerical integration to localize the pseudopotential. {copyright} {ital 1996 American Institute of Physics.}

  18. Monte Carlo Shower Counter Studies

    NASA Technical Reports Server (NTRS)

    Snyder, H. David

    1991-01-01

    Activities and accomplishments related to the Monte Carlo shower counter studies are summarized. A tape of the VMS version of the GEANT software was obtained and installed on the central computer at Gallaudet University. Due to difficulties encountered in updating this VMS version, a decision was made to switch to the UNIX version of the package. This version was installed and used to generate the set of data files currently accessed by various analysis programs. The GEANT software was used to write files of data for positron and proton showers. Showers were simulated for a detector consisting of 50 alternating layers of lead and scintillator. Each file consisted of 1000 events at each of the following energies: 0.1, 0.5, 2.0, 10, 44, and 200 GeV. Data analysis activities related to clustering, chi square, and likelihood analyses are summarized. Source code for the GEANT user subprograms and data analysis programs are provided along with example data plots.

  19. Improved Monte Carlo Renormalization Group Method

    DOE R&D Accomplishments Database

    Gupta, R.; Wilson, K. G.; Umrigar, C.

    1985-01-01

    An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.

  20. Monte Carlo Ion Transport Analysis Code.

    2009-04-15

    Version: 00 TRIPOS is a versatile Monte Carlo ion transport analysis code. It has been applied to the treatment of both surface and bulk radiation effects. The media considered is composed of multilayer polyatomic materials.

  1. Monte Carlo Transport for Electron Thermal Transport

    NASA Astrophysics Data System (ADS)

    Chenhall, Jeffrey; Cao, Duc; Moses, Gregory

    2015-11-01

    The iSNB (implicit Schurtz Nicolai Busquet multigroup electron thermal transport method of Cao et al. is adapted into a Monte Carlo transport method in order to better model the effects of non-local behavior. The end goal is a hybrid transport-diffusion method that combines Monte Carlo Transport with a discrete diffusion Monte Carlo (DDMC). The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the method will be presented. This work was supported by Sandia National Laboratory - Albuquerque and the University of Rochester Laboratory for Laser Energetics.

  2. Quantum Monte Carlo calculations of electromagnetic moments and transitions in A{<=}9 nuclei including meson-exchange currents derived from chiral effective field theory

    SciTech Connect

    Saori Pastore, S.C. Pieper, Rocco Schiavilla, Robert Wiringa

    2013-03-01

    Quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for A{<=}9 nuclei. The realistic Argonne v{sub 18} two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and M1 transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the A=9, T=3/2 systems, in which they provide up to ~20% (~40%) of the total predicted value for the {sup 9}Li ({sup 9}C) magnetic moment.

  3. Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction.

    PubMed

    Shepherd, James J; Henderson, Thomas M; Scuseria, Gustavo E

    2016-03-01

    Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure. PMID:26957162

  4. Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

    NASA Astrophysics Data System (ADS)

    Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.

    2016-03-01

    Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.

  5. Equations of state and stability of MgSiO3 perovskite and post-perovskite phases from quantum Monte Carlo simulations

    SciTech Connect

    Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim

    2014-11-10

    In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO3 agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from our QMC equations of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.

  6. (1)H NMR z-spectra of acetate methyl in stretched hydrogels: quantum-mechanical description and Markov chain Monte Carlo relaxation-parameter estimation.

    PubMed

    Shishmarev, Dmitry; Chapman, Bogdan E; Naumann, Christoph; Mamone, Salvatore; Kuchel, Philip W

    2015-01-01

    The (1)H NMR signal of the methyl group of sodium acetate is shown to be a triplet in the anisotropic environment of stretched gelatin gel. The multiplet structure of the signal is due to the intra-methyl residual dipolar couplings. The relaxation properties of the spin system were probed by recording steady-state irradiation envelopes ('z-spectra'). A quantum-mechanical model based on irreducible spherical tensors formed by the three magnetically equivalent spins of the methyl group was used to simulate and fit experimental z-spectra. The multiple parameter values of the relaxation model were estimated by using a Bayesian-based Markov chain Monte Carlo algorithm. PMID:25486634

  7. Equations of state and stability of MgSiO3 perovskite and post-perovskite phases from quantum Monte Carlo simulations

    DOE PAGESBeta

    Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim

    2014-11-10

    In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO3 agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from our QMC equationsmore » of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.« less

  8. Benchmark quantum Monte Carlo calculations of the ground-state kinetic, interaction and total energy of the three-dimensional electron gas.

    PubMed

    Gurtubay, I G; Gaudoin, R; Pitarke, J M

    2010-02-17

    We report variational and diffusion quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N = 54, 102, 178, and 226 electrons. We remove finite-size effects by extrapolation and we find lower energies than previously reported. Using the Hellman-Feynman operator sampling method introduced in Gaudoin and Pitarke (2007 Phys. Rev. Lett. 99 126406), we compute accurately, within the fixed-node approximation, the separate kinetic and interaction contributions to the total ground-state energy. The difference between the interaction energies obtained from the original Slater-determinant nodes and the backflow-displaced nodes is found to be considerably larger than the difference between the corresponding kinetic energies. PMID:21389370

  9. Extra Chance Generalized Hybrid Monte Carlo

    NASA Astrophysics Data System (ADS)

    Campos, Cédric M.; Sanz-Serna, J. M.

    2015-01-01

    We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefully, may be accepted. We present experiments that clearly indicate that the additional work per sample carried out in the extra chance approach clearly pays in terms of the quality of the samples generated.

  10. Monte Carlo simulations of phosphate polyhedron connectivity in glasses

    SciTech Connect

    ALAM,TODD M.

    2000-01-01

    Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.

  11. Monte Carlo Simulations of Phosphate Polyhedron Connectivity in Glasses

    SciTech Connect

    ALAM,TODD M.

    1999-12-21

    Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.

  12. Monte Carlo simulation in statistical physics: an introduction

    NASA Astrophysics Data System (ADS)

    Binder, K., Heermann, D. W.

    Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. This fourth edition has been updated and a new chapter on Monte Carlo simulation of quantum-mechanical problems has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001.

  13. Quantum Monte Carlo study of hard-core bosons in a pyrochlore lattice with six-site ring-exchange interactions

    NASA Astrophysics Data System (ADS)

    Tieman, Catherine; Rousseau, Valery

    Highly frustrated quantum systems on lattices can exhibit a wide variety of phases. In addition to the usual Mott insulating and superfluid phases, these systems can also produce some so-called ``exotic phases'', such as super-solid and valence-bond-solid phases. An example of particularly frustrated lattice is the pyrochlore structure, which is formed by corner-sharing tetrahedrons. Many real materials adopt this structure, for instance the crystal Cd2 Re2O7 , which exhibits superconducting properties. However, the complex structure of these materials combined with the complexity of the dominant interactions that describe them makes their analytical study difficult. Also, approximate methods, such as mean-field theory, fail to give a correct description of these systems. In this work, we report on the first exact quantum Monte Carlo study of a model of hard-core bosons in a pyrochlore lattice with six-site ring-exchange interactions, using the Stochastic Green Function (SGF) algorithm. We analyze the superfluid density and the structure factor as functions of the filling and ring-exchange interaction strength, and we map out the ground state phase diagram.

  14. Spatial Correlations in Monte Carlo Criticality Simulations

    NASA Astrophysics Data System (ADS)

    Dumonteil, E.; Malvagi, F.; Zoia, A.; Mazzolo, A.; Artusio, D.; Dieudonné, C.; De Mulatier, C.

    2014-06-01

    Temporal correlations arising in Monte Carlo criticality codes have focused the attention of both developers and practitioners for a long time. Those correlations affects the evaluation of tallies of loosely coupled systems, where the system's typical size is very large compared to the diffusion/absorption length scale of the neutrons. These time correlations are closely related to spatial correlations, both variables being linked by the transport equation. Therefore this paper addresses the question of diagnosing spatial correlations in Monte Carlo criticality simulations. In that aim, we will propose a spatial correlation function well suited to Monte Carlo simulations, and show its use while simulating a fuel pin-cell. The results will be discussed, modeled and interpreted using the tools of branching processes of statistical mechanics. A mechanism called "neutron clustering", affecting simulations, will be discussed in this frame.

  15. Geodesic Monte Carlo on Embedded Manifolds.

    PubMed

    Byrne, Simon; Girolami, Mark

    2013-12-01

    Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton-Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

  16. Monte Carlo dose computation for IMRT optimization*

    NASA Astrophysics Data System (ADS)

    Laub, W.; Alber, M.; Birkner, M.; Nüsslin, F.

    2000-07-01

    A method which combines the accuracy of Monte Carlo dose calculation with a finite size pencil-beam based intensity modulation optimization is presented. The pencil-beam algorithm is employed to compute the fluence element updates for a converging sequence of Monte Carlo dose distributions. The combination is shown to improve results over the pencil-beam based optimization in a lung tumour case and a head and neck case. Inhomogeneity effects like a broader penumbra and dose build-up regions can be compensated for by intensity modulation.

  17. Monte Carlo simulation of neutron scattering instruments

    SciTech Connect

    Seeger, P.A.

    1995-12-31

    A library of Monte Carlo subroutines has been developed for the purpose of design of neutron scattering instruments. Using small-angle scattering as an example, the philosophy and structure of the library are described and the programs are used to compare instruments at continuous wave (CW) and long-pulse spallation source (LPSS) neutron facilities. The Monte Carlo results give a count-rate gain of a factor between 2 and 4 using time-of-flight analysis. This is comparable to scaling arguments based on the ratio of wavelength bandwidth to resolution width.

  18. Monte Carlo simulation of an expanding gas

    NASA Technical Reports Server (NTRS)

    Boyd, Iain D.

    1989-01-01

    By application of simple computer graphics techniques, the statistical performance of two Monte Carlo methods used in the simulation of rarefied gas flows are assessed. Specifically, two direct simulation Monte Carlo (DSMC) methods developed by Bird and Nanbu are considered. The graphics techniques are found to be of great benefit in the reduction and interpretation of the large volume of data generated, thus enabling important conclusions to be drawn about the simulation results. Hence, it is discovered that the method of Nanbu suffers from increased statistical fluctuations, thereby prohibiting its use in the solution of practical problems.

  19. Geodesic Monte Carlo on Embedded Manifolds

    PubMed Central

    Byrne, Simon; Girolami, Mark

    2013-01-01

    Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

  20. Monte Carlo simulation of a quantum noise limited Čerenkov detector based on air-spaced light guiding taper for megavoltage x-ray imaging

    SciTech Connect

    Teymurazyan, A.; Rowlands, J. A.; Pang, G.

    2014-04-15

    Purpose: Electronic Portal Imaging Devices (EPIDs) have been widely used in radiation therapy and are still needed on linear accelerators (Linacs) equipped with kilovoltage cone beam CT (kV-CBCT) or MRI systems. Our aim is to develop a new high quantum efficiency (QE) Čerenkov Portal Imaging Device (CPID) that is quantum noise limited at dose levels corresponding to a single Linac pulse. Methods: Recently a new concept of CPID for MV x-ray imaging in radiation therapy was introduced. It relies on Čerenkov effect for x-ray detection. The proposed design consisted of a matrix of optical fibers aligned with the incident x-rays and coupled to an active matrix flat panel imager (AMFPI) for image readout. A weakness of such design is that too few Čerenkov light photons reach the AMFPI for each incident x-ray and an AMFPI with an avalanche gain is required in order to overcome the readout noise for portal imaging application. In this work the authors propose to replace the optical fibers in the CPID with light guides without a cladding layer that are suspended in air. The air between the light guides takes on the role of the cladding layer found in a regular optical fiber. Since air has a significantly lower refractive index (∼1 versus 1.38 in a typical cladding layer), a much superior light collection efficiency is achieved. Results: A Monte Carlo simulation of the new design has been conducted to investigate its feasibility. Detector quantities such as quantum efficiency (QE), spatial resolution (MTF), and frequency dependent detective quantum efficiency (DQE) have been evaluated. The detector signal and the quantum noise have been compared to the readout noise. Conclusions: Our studies show that the modified new CPID has a QE and DQE more than an order of magnitude greater than that of current clinical systems and yet a spatial resolution similar to that of current low-QE flat-panel based EPIDs. Furthermore it was demonstrated that the new CPID does not require an

  1. A quasi-Monte Carlo Metropolis algorithm

    PubMed Central

    Owen, Art B.; Tribble, Seth D.

    2005-01-01

    This work presents a version of the Metropolis–Hastings algorithm using quasi-Monte Carlo inputs. We prove that the method yields consistent estimates in some problems with finite state spaces and completely uniformly distributed inputs. In some numerical examples, the proposed method is much more accurate than ordinary Metropolis–Hastings sampling. PMID:15956207

  2. Monte Carlo methods in genetic analysis

    SciTech Connect

    Lin, Shili

    1996-12-31

    Many genetic analyses require computation of probabilities and likelihoods of pedigree data. With more and more genetic marker data deriving from new DNA technologies becoming available to researchers, exact computations are often formidable with standard statistical methods and computational algorithms. The desire to utilize as much available data as possible, coupled with complexities of realistic genetic models, push traditional approaches to their limits. These methods encounter severe methodological and computational challenges, even with the aid of advanced computing technology. Monte Carlo methods are therefore increasingly being explored as practical techniques for estimating these probabilities and likelihoods. This paper reviews the basic elements of the Markov chain Monte Carlo method and the method of sequential imputation, with an emphasis upon their applicability to genetic analysis. Three areas of applications are presented to demonstrate the versatility of Markov chain Monte Carlo for different types of genetic problems. A multilocus linkage analysis example is also presented to illustrate the sequential imputation method. Finally, important statistical issues of Markov chain Monte Carlo and sequential imputation, some of which are unique to genetic data, are discussed, and current solutions are outlined. 72 refs.

  3. Structural Reliability and Monte Carlo Simulation.

    ERIC Educational Resources Information Center

    Laumakis, P. J.; Harlow, G.

    2002-01-01

    Analyzes a simple boom structure and assesses its reliability using elementary engineering mechanics. Demonstrates the power and utility of Monte-Carlo simulation by showing that such a simulation can be implemented more readily with results that compare favorably to the theoretical calculations. (Author/MM)

  4. MCMAC: Monte Carlo Merger Analysis Code

    NASA Astrophysics Data System (ADS)

    Dawson, William A.

    2014-07-01

    Monte Carlo Merger Analysis Code (MCMAC) aids in the study of merging clusters. It takes observed priors on each subcluster's mass, radial velocity, and projected separation, draws randomly from those priors, and uses them in a analytic model to get posterior PDF's for merger dynamic properties of interest (e.g. collision velocity, time since collision).

  5. A comparison of Monte Carlo generators

    NASA Astrophysics Data System (ADS)

    Golan, Tomasz

    2015-05-01

    A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and π+ two-dimensional energy vs cosine distribution.

  6. Monte Carlo simulations of lattice gauge theories

    SciTech Connect

    Rebbi, C

    1980-02-01

    Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)

  7. A comparison of Monte Carlo generators

    SciTech Connect

    Golan, Tomasz

    2015-05-15

    A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and π{sup +} two-dimensional energy vs cosine distribution.

  8. Scalable Domain Decomposed Monte Carlo Particle Transport

    SciTech Connect

    O'Brien, Matthew Joseph

    2013-12-05

    In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation.

  9. Monte Carlo methods: Application to hydrogen gas and hard spheres

    NASA Astrophysics Data System (ADS)

    Dewing, Mark Douglas

    2001-08-01

    Quantum Monte Carlo (QMC) methods are among the most accurate for computing ground state properties of quantum systems. The two major types of QMC we use are Variational Monte Carlo (VMC), which evaluates integrals arising from the variational principle, and Diffusion Monte Carlo (DMC), which stochastically projects to the ground state from a trial wave function. These methods are applied to a system of boson hard spheres to get exact, infinite system size results for the ground state at several densities. The kinds of problems that can be simulated with Monte Carlo methods are expanded through the development of new algorithms for combining a QMC simulation with a classical Monte Carlo simulation, which we call Coupled Electronic-Ionic Monte Carlo (CEIMC). The new CEIMC method is applied to a system of molecular hydrogen at temperatures ranging from 2800K to 4500K and densities from 0.25 to 0.46 g/cm3. VMC requires optimizing a parameterized wave function to find the minimum energy. We examine several techniques for optimizing VMC wave functions, focusing on the ability to optimize parameters appearing in the Slater determinant. Classical Monte Carlo simulations use an empirical interatomic potential to compute equilibrium properties of various states of matter. The CEIMC method replaces the empirical potential with a QMC calculation of the electronic energy. This is similar in spirit to the Car-Parrinello technique, which uses Density Functional Theory for the electrons and molecular dynamics for the nuclei. The challenges in constructing an efficient CEIMC simulation center mostly around the noisy results generated from the QMC computations of the electronic energy. We introduce two complementary techniques, one for tolerating the noise and the other for reducing it. The penalty method modifies the Metropolis acceptance ratio to tolerate noise without introducing a bias in the simulation of the nuclei. For reducing the noise, we introduce the two-sided energy

  10. Monte Carlo: in the beginning and some great expectations

    SciTech Connect

    Metropolis, N.

    1985-01-01

    The central theme will be on the historical setting and origins of the Monte Carlo Method. The scene was post-war Los Alamos Scientific Laboratory. There was an inevitability about the Monte Carlo Event: the ENIAC had recently enjoyed its meteoric rise (on a classified Los Alamos problem); Stan Ulam had returned to Los Alamos; John von Neumann was a frequent visitor. Techniques, algorithms, and applications developed rapidly at Los Alamos. Soon, the fascination of the Method reached wider horizons. The first paper was submitted for publication in the spring of 1949. In the summer of 1949, the first open conference was held at the University of California at Los Angeles. Of some interst perhaps is an account of Fermi's earlier, independent application in neutron moderation studies while at the University of Rome. The quantum leap expected with the advent of massively parallel processors will provide stimuli for very ambitious applications of the Monte Carlo Method in disciplines ranging from field theories to cosmology, including more realistic models in the neurosciences. A structure of multi-instruction sets for parallel processing is ideally suited for the Monte Carlo approach. One may even hope for a modest hardening of the soft sciences.

  11. Observations on variational and projector Monte Carlo methods

    SciTech Connect

    Umrigar, C. J.

    2015-10-28

    Variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.

  12. A quantum Monte Carlo study on electron correlation in all-metal aromatic clusters MAl4(-) (M = Li, Na, K, Rb, Cu, Ag and Au).

    PubMed

    Brito, Bráulio Gabriel A; Hai, G-Q; Teixeira Rabelo, J N; Cândido, Ladir

    2014-05-14

    Using fixed-node diffusion quantum Monte Carlo (FN-DMC) simulation we investigate the electron correlation in all-metal aromatic clusters MAl4(-) (with M = Li, Na, K, Rb, Cu, Ag and Au). The electron detachment energies and electron affinities of the clusters are obtained. The vertical electron detachment energies obtained from the FN-DMC calculations are in very good agreement with the available experimental results. Calculations are also performed within the Hartree-Fock approximation, density-functional theory (DFT), and the couple-cluster (CCSD(T)) method. From the obtained results, we analyse the impact of the electron correlation effects in these bimetallic clusters and find that the correlation of the valence electrons contributes significantly to the detachment energies and electron affinities, varying between 20% and 50% of their total values. Furthermore, we discuss the electron correlation effects on the stability of the clusters as well as the accuracy of the DFT and CCSD(T) calculations in the present systems. PMID:24676470

  13. Using quantum Monte Carlo for the interaction of water with carbon and BN based substrates and assessing exchange-correlation functionals

    NASA Astrophysics Data System (ADS)

    Al-Hamdani, Yasmine; Alfe, Dario; von Lilienfeld, O. Anatole; Michaelides, Angelos

    The interaction of water with the pure surfaces, graphene and hexagonal boron nitride (h- BN), has received a lot of attention because of interesting phenomena exhibited by these systems and their promising potential applications in clean energy, water purification, hydrogen storage, and bio-sensing. BN doped graphene can also now be made, opening the way to carefully designed hybrid materials. However, much of the fundamental mechanisms regarding the interaction between these surfaces and water is still not well understood. We use quantum Monte Carlo to establish accurate benchmarks for water on a number of carbonaceous and BN based substrates, including 2-dimensional periodic surfaces, for which van der Waals interactions play a key role. The benchmarks are then used to test and understand various exchange-correlation functionals in density functional theory. We find that the physisorption of water is poorly described in terms of the adsorption site and the interaction energy by a range of different classes of exchange- correlation functionals, including some that account for dispersion, and we show where these inadequacies might come from.

  14. The Numerical Comparison of Magnetic Susceptibility and Heat Capacity of TMNIN with the Result of a Quantum Monte Carlo Method for the Haldane System

    NASA Astrophysics Data System (ADS)

    Ito, Masakazu; Mito, Masaki; Deguchi, Hiroyuki; Takeda, Kazuyoshi

    1994-03-01

    The measurements of magnetic heat capacity and susceptibility of one-dimensional S=1 antiferromagnet (CH3)4NNi(NO2)3 (TMNIN) have been carried out in order to make comparison with the theoretical results of a quantum Monte Carlo method for the Haldane system. The results for the heat capacity, which show a broad maximum around 10 K, are well reproduced by the theory with the interaction J/k B=-12.0±1.0 K in the temperature range T>0.2\\mid J\\mid S(S+1)/k_B. The low temperature heat capacity exhibits an exponential decay with gap energy Δ/k B=5.3±0.2 K, which gives {\\mitΔ}=0.44\\mid J\\mid , in contrast to the linear dependence on temperature as in the case for half integer spin. The residual magnetic entropy below 0.7 K is estimated to be 0.07% of Nk B ln 3, which denies the possibility of three-dimensional ordering of the spin system at lower temperatures. The observed susceptibility also agrees with the theory with J/k B=-10.9 K and g=2.02 in the whole temperature region, when we take the effect from the finite length of the chains into consideration.

  15. Quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be with meson-exchange currents derived from chiral effective field theory

    SciTech Connect

    Pastore, S.; Wiringa, Robert B.; Pieper, Steven C.; Schiavilla, Rocco

    2014-08-01

    We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.

  16. Solvent effects on the absorption spectrum and first hyperpolarizability of keto-enol tautomeric forms of anil derivatives: A Monte Carlo/quantum mechanics study

    NASA Astrophysics Data System (ADS)

    Adriano Junior, L.; Fonseca, T. L.; Castro, M. A.

    2016-06-01

    Theoretical results for the absorption spectrum and electric properties of the enol and keto tautomeric forms of anil derivatives in the gas-phase and in solution are presented. The electronic properties in chloroform, acetonitrile, methanol, and water were determined by carrying out sequential Monte Carlo simulations and quantum mechanics calculations based on the time dependent density functional theory and on the second-order Møller-Plesset perturbation theory method. The results illustrate the role played by electrostatic interactions in the electronic properties of anil derivatives in a liquid environment. There is a significant increase of the dipole moment in solution (20%-100%) relative to the gas-phase value. Solvent effects are mild for the absorption spectrum and linear polarizability but they can be particularly important for first hyperpolarizability. A large first hyperpolarizability contrast between the enol and keto forms is observed when absorption spectra present intense lowest-energy absorption bands. Dynamic results for the first hyperpolarizability are in qualitative agreement with the available experimental results.

  17. Solvent effects on the absorption spectrum and first hyperpolarizability of keto-enol tautomeric forms of anil derivatives: A Monte Carlo/quantum mechanics study.

    PubMed

    Adriano Junior, L; Fonseca, T L; Castro, M A

    2016-06-21

    Theoretical results for the absorption spectrum and electric properties of the enol and keto tautomeric forms of anil derivatives in the gas-phase and in solution are presented. The electronic properties in chloroform, acetonitrile, methanol, and water were determined by carrying out sequential Monte Carlo simulations and quantum mechanics calculations based on the time dependent density functional theory and on the second-order Møller-Plesset perturbation theory method. The results illustrate the role played by electrostatic interactions in the electronic properties of anil derivatives in a liquid environment. There is a significant increase of the dipole moment in solution (20%-100%) relative to the gas-phase value. Solvent effects are mild for the absorption spectrum and linear polarizability but they can be particularly important for first hyperpolarizability. A large first hyperpolarizability contrast between the enol and keto forms is observed when absorption spectra present intense lowest-energy absorption bands. Dynamic results for the first hyperpolarizability are in qualitative agreement with the available experimental results. PMID:27334183

  18. Sign-Problem-Free Quantum Monte Carlo Study on Thermodynamic Properties and Magnetic Phase Transitions in Orbital-Active Itinerant Ferromagnets

    NASA Astrophysics Data System (ADS)

    Xu, Shenglong; Li, Yi; Wu, Congjun

    2015-04-01

    The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of nonperturbative methods to handle strong magnetic fluctuations of itinerant electrons. We nonpertubatively study thermodynamic properties and magnetic phase transitions of a two-dimensional multiorbital Hubbard model exhibiting ferromagnetic ground states. Quantum Monte Carlo simulations are employed, which are proved in a wide density region free of the sign problem usually suffered by simulations for fermions. Both Hund's coupling and electron itinerancy are essential for establishing the ferromagnetic coherence. No local magnetic moments exist in the system as a priori; nevertheless, the spin channel remains incoherent showing the Curie-Weiss-type spin magnetic susceptibility down to very low temperatures at which the charge channel is already coherent, exhibiting a weakly temperature-dependent compressibility. For the SU(2) invariant systems, the spin susceptibility further grows exponentially as approaching zero temperature in two dimensions. In the paramagnetic phase close to the Curie temperature, the momentum space Fermi distributions exhibit strong resemblance to those in the fully polarized state. The long-range ferromagnetic ordering appears when the symmetry is reduced to the Ising class, and the Curie temperature is accurately determined. These simulations provide helpful guidance to searching for novel ferromagnetic materials in both strongly correlated d -orbital transition-metal oxide layers and the p -orbital ultracold atom optical lattice systems.

  19. A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets.

    PubMed

    Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei

    2007-05-21

    The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values. PMID:17523796

  20. Synergies from using higher order symplectic decompositions both for ordinary differential equations and quantum Monte Carlo methods

    SciTech Connect

    Matuttis, Hans-Georg; Wang, Xiaoxing

    2015-03-10

    Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.

  1. Low-energy cross-section calculations of single molecules by electron impact: a classical Monte Carlo transport approach with quantum mechanical description

    NASA Astrophysics Data System (ADS)

    Madsen, J. R.; Akabani, G.

    2014-05-01

    The present state of modeling radio-induced effects at the cellular level does not account for the microscopic inhomogeneity of the nucleus from the non-aqueous contents (i.e. proteins, DNA) by approximating the entire cellular nucleus as a homogenous medium of water. Charged particle track-structure calculations utilizing this approximation are therefore neglecting to account for approximately 30% of the molecular variation within the nucleus. To truly understand what happens when biological matter is irradiated, charged particle track-structure calculations need detailed knowledge of the secondary electron cascade, resulting from interactions with not only the primary biological component—water--but also the non-aqueous contents, down to very low energies. This paper presents our work on a generic approach for calculating low-energy interaction cross-sections between incident charged particles and individual molecules. The purpose of our work is to develop a self-consistent computational method for predicting molecule-specific interaction cross-sections, such as the component molecules of DNA and proteins (i.e. nucleotides and amino acids), in the very low-energy regime. These results would then be applied in a track-structure code and thereby reduce the homogenous water approximation. The present methodology—inspired by seeking a combination of the accuracy of quantum mechanics and the scalability, robustness, and flexibility of Monte Carlo methods—begins with the calculation of a solution to the many-body Schrödinger equation and proceeds to use Monte Carlo methods to calculate the perturbations in the internal electron field to determine the interaction processes, such as ionization and excitation. As a test of our model, the approach is applied to a water molecule in the same method as it would be applied to a nucleotide or amino acid and compared with the low-energy cross-sections from the GEANT4-DNA physics package of the Geant4 simulation toolkit

  2. Porphyrins as Corrosion Inhibitors for N80 Steel in 3.5% NaCl Solution: Electrochemical, Quantum Chemical, QSAR and Monte Carlo Simulations Studies.

    PubMed

    Singh, Ambrish; Lin, Yuanhua; Quraishi, Mumtaz A; Olasunkanmi, Lukman O; Fayemi, Omolola E; Sasikumar, Yesudass; Ramaganthan, Baskar; Bahadur, Indra; Obot, Ime B; Adekunle, Abolanle S; Kabanda, Mwadham M; Ebenso, Eno E

    2015-01-01

    The inhibition of the corrosion of N80 steel in 3.5 wt. % NaCl solution saturated with CO2 by four porphyrins, namely 5,10,15,20-tetrakis(4-hydroxyphenyl)-21H,23H-porphyrin (HPTB), 5,10,15,20-tetra(4-pyridyl)-21H,23H-porphyrin (T4PP), 4,4',4″,4‴-(porphyrin-5,10,15,20-tetrayl)tetrakis(benzoic acid) (THP) and 5,10,15,20-tetraphenyl-21H,23H-porphyrin (TPP) was studied using electrochemical impedance spectroscopy (EIS), potentiodynamic polarization, scanning electrochemical microscopy (SECM) and scanning electron microscopy (SEM) techniques. The results showed that the inhibition efficiency, η% increases with increasing concentration of the inhibitors. The EIS results revealed that the N80 steel surface with adsorbed porphyrins exhibited non-ideal capacitive behaviour with reduced charge transfer activity. Potentiodynamic polarization measurements indicated that the studied porphyrins acted as mixed type inhibitors. The SECM results confirmed the adsorption of the porphyrins on N80 steel thereby forming a relatively insulated surface. The SEM also confirmed the formation of protective films of the porphyrins on N80 steel surface thereby protecting the surface from direct acid attack. Quantum chemical calculations, quantitative structure activity relationship (QSAR) were also carried out on the studied porphyrins and the results showed that the corrosion inhibition performances of the porphyrins could be related to their EHOMO, ELUMO, ω, and μ values. Monte Carlo simulation studies showed that THP has the highest adsorption energy, while T4PP has the least adsorption energy in agreement with the values of σ from quantum chemical calculations. PMID:26295223

  3. Path integral Monte Carlo and the electron gas

    NASA Astrophysics Data System (ADS)

    Brown, Ethan W.

    Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational

  4. Path integral Monte Carlo on a lattice: extended states.

    PubMed

    O'Callaghan, Mark; Miller, Bruce N

    2014-04-01

    The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential ε, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations. PMID:24827210

  5. Status of Monte Carlo at Los Alamos

    SciTech Connect

    Thompson, W.L.; Cashwell, E.D.

    1980-01-01

    At Los Alamos the early work of Fermi, von Neumann, and Ulam has been developed and supplemented by many followers, notably Cashwell and Everett, and the main product today is the continuous-energy, general-purpose, generalized-geometry, time-dependent, coupled neutron-photon transport code called MCNP. The Los Alamos Monte Carlo research and development effort is concentrated in Group X-6. MCNP treats an arbitrary three-dimensional configuration of arbitrary materials in geometric cells bounded by first- and second-degree surfaces and some fourth-degree surfaces (elliptical tori). Monte Carlo has evolved into perhaps the main method for radiation transport calculations at Los Alamos. MCNP is used in every technical division at the Laboratory by over 130 users about 600 times a month accounting for nearly 200 hours of CDC-7600 time.

  6. An enhanced Monte Carlo outlier detection method.

    PubMed

    Zhang, Liangxiao; Li, Peiwu; Mao, Jin; Ma, Fei; Ding, Xiaoxia; Zhang, Qi

    2015-09-30

    Outlier detection is crucial in building a highly predictive model. In this study, we proposed an enhanced Monte Carlo outlier detection method by establishing cross-prediction models based on determinate normal samples and analyzing the distribution of prediction errors individually for dubious samples. One simulated and three real datasets were used to illustrate and validate the performance of our method, and the results indicated that this method outperformed Monte Carlo outlier detection in outlier diagnosis. After these outliers were removed, the value of validation by Kovats retention indices and the root mean square error of prediction decreased from 3.195 to 1.655, and the average cross-validation prediction error decreased from 2.0341 to 1.2780. This method helps establish a good model by eliminating outliers. © 2015 Wiley Periodicals, Inc. PMID:26226927

  7. Status of Monte Carlo at Los Alamos

    SciTech Connect

    Thompson, W.L.; Cashwell, E.D.; Godfrey, T.N.K.; Schrandt, R.G.; Deutsch, O.L.; Booth, T.E.

    1980-05-01

    Four papers were presented by Group X-6 on April 22, 1980, at the Oak Ridge Radiation Shielding Information Center (RSIC) Seminar-Workshop on Theory and Applications of Monte Carlo Methods. These papers are combined into one report for convenience and because they are related to each other. The first paper (by Thompson and Cashwell) is a general survey about X-6 and MCNP and is an introduction to the other three papers. It can also serve as a resume of X-6. The second paper (by Godfrey) explains some of the details of geometry specification in MCNP. The third paper (by Cashwell and Schrandt) illustrates calculating flux at a point with MCNP; in particular, the once-more-collided flux estimator is demonstrated. Finally, the fourth paper (by Thompson, Deutsch, and Booth) is a tutorial on some variance-reduction techniques. It should be required for a fledging Monte Carlo practitioner.

  8. Monte Carlo Methods in the Physical Sciences

    SciTech Connect

    Kalos, M H

    2007-06-06

    I will review the role that Monte Carlo methods play in the physical sciences. They are very widely used for a number of reasons: they permit the rapid and faithful transformation of a natural or model stochastic process into a computer code. They are powerful numerical methods for treating the many-dimensional problems that derive from important physical systems. Finally, many of the methods naturally permit the use of modern parallel computers in efficient ways. In the presentation, I will emphasize four aspects of the computations: whether or not the computation derives from a natural or model stochastic process; whether the system under study is highly idealized or realistic; whether the Monte Carlo methodology is straightforward or mathematically sophisticated; and finally, the scientific role of the computation.

  9. Fast Lattice Monte Carlo Simulations of Polymers

    NASA Astrophysics Data System (ADS)

    Wang, Qiang; Zhang, Pengfei

    2014-03-01

    The recently proposed fast lattice Monte Carlo (FLMC) simulations (with multiple occupancy of lattice sites (MOLS) and Kronecker δ-function interactions) give much faster/better sampling of configuration space than both off-lattice molecular simulations (with pair-potential calculations) and conventional lattice Monte Carlo simulations (with self- and mutual-avoiding walk and nearest-neighbor interactions) of polymers.[1] Quantitative coarse-graining of polymeric systems can also be performed using lattice models with MOLS.[2] Here we use several model systems, including polymer melts, solutions, blends, as well as confined and/or grafted polymers, to demonstrate the great advantages of FLMC simulations in the study of equilibrium properties of polymers.

  10. Monte-Carlo Opening Books for Amazons

    NASA Astrophysics Data System (ADS)

    Kloetzer, Julien

    Automatically creating opening books is a natural step towards the building of strong game-playing programs, especially when there is little available knowledge about the game. However, while recent popular Monte-Carlo Tree-Search programs showed strong results for various games, we show here that programs based on such methods cannot efficiently use opening books created using algorithms based on minimax. To overcome this issue, we propose to use an MCTS-based technique, Meta-MCTS, to create such opening books. This method, while requiring some tuning to arrive at the best opening book possible, shows promising results to create an opening book for the game of the Amazons, even if this is at the cost of removing its Monte-Carlo part.

  11. Monte Carlo modeling of exospheric bodies - Mercury

    NASA Technical Reports Server (NTRS)

    Smith, G. R.; Broadfoot, A. L.; Wallace, L.; Shemansky, D. E.

    1978-01-01

    In order to study the interaction with the surface, a Monte Carlo program is developed to determine the distribution with altitude as well as the global distribution of density at the surface in a single operation. The analysis presented shows that the appropriate source distribution should be Maxwell-Boltzmann flux if the particles in the distribution are to be treated as components of flux. Monte Carlo calculations with a Maxwell-Boltzmann flux source are compared with Mariner 10 UV spectrometer data. Results indicate that the presently operating models are not capable of fitting the observed Mercury exosphere. It is suggested that an atmosphere calculated with a barometric source distribution is suitable for more realistic future exospheric models.

  12. Estimation of beryllium ground state energy by Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Kabir, K. M. Ariful; Halder, Amal

    2015-05-01

    Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.

  13. Nuclear pairing within a configuration-space Monte Carlo approach

    NASA Astrophysics Data System (ADS)

    Lingle, Mark; Volya, Alexander

    2015-06-01

    Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.

  14. Estimation of beryllium ground state energy by Monte Carlo simulation

    SciTech Connect

    Kabir, K. M. Ariful; Halder, Amal

    2015-05-15

    Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.

  15. Quantum Monte Carlo study of a one-dimensional phase-fluctuating condensate in a harmonic trap

    SciTech Connect

    Gils, C.; Pollet, L.; Troyer, M.; Vernier, A.; Hebert, F.; Batrouni, G. G.

    2007-06-15

    We study numerically the low-temperature behavior of a one-dimensional Bose gas trapped in an optical lattice. For a sufficient number of particles and weak repulsive interactions, we find a clear regime of temperatures where density fluctuations are negligible but phase fluctuations are considerable, i.e., a quasicondensate. In the weakly interacting limit, our results are in very good agreement with those obtained using a mean-field approximation. In coupling regimes beyond the validity of mean-field approaches, a phase-fluctuating condensate also appears, but the phase-correlation properties are qualitatively different. It is shown that quantum depletion plays an important role.

  16. Inhomogeneous Monte Carlo simulations of dermoscopic spectroscopy

    NASA Astrophysics Data System (ADS)

    Gareau, Daniel S.; Li, Ting; Jacques, Steven; Krueger, James

    2012-03-01

    Clinical skin-lesion diagnosis uses dermoscopy: 10X epiluminescence microscopy. Skin appearance ranges from black to white with shades of blue, red, gray and orange. Color is an important diagnostic criteria for diseases including melanoma. Melanin and blood content and distribution impact the diffuse spectral remittance (300-1000nm). Skin layers: immersion medium, stratum corneum, spinous epidermis, basal epidermis and dermis as well as laterally asymmetric features (eg. melanocytic invasion) were modeled in an inhomogeneous Monte Carlo model.

  17. Monte Carlo simulation of Alaska wolf survival

    NASA Astrophysics Data System (ADS)

    Feingold, S. J.

    1996-02-01

    Alaskan wolves live in a harsh climate and are hunted intensively. Penna's biological aging code, using Monte Carlo methods, has been adapted to simulate wolf survival. It was run on the case in which hunting causes the disruption of wolves' social structure. Social disruption was shown to increase the number of deaths occurring at a given level of hunting. For high levels of social disruption, the population did not survive.

  18. Numerical reproducibility for implicit Monte Carlo simulations

    SciTech Connect

    Cleveland, M.; Brunner, T.; Gentile, N.

    2013-07-01

    We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. In [1], a way of eliminating this roundoff error using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. A non-arbitrary precision approaches required a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step. (authors)

  19. jTracker and Monte Carlo Comparison

    NASA Astrophysics Data System (ADS)

    Selensky, Lauren; SeaQuest/E906 Collaboration

    2015-10-01

    SeaQuest is designed to observe the characteristics and behavior of `sea-quarks' in a proton by reconstructing them from the subatomic particles produced in a collision. The 120 GeV beam from the main injector collides with a fixed target and then passes through a series of detectors which records information about the particles produced in the collision. However, this data becomes meaningful only after it has been processed, stored, analyzed, and interpreted. Several programs are involved in this process. jTracker (sqerp) reads wire or hodoscope hits and reconstructs the tracks of potential dimuon pairs from a run, and Geant4 Monte Carlo simulates dimuon production and background noise from the beam. During track reconstruction, an event must meet the criteria set by the tracker to be considered a viable dimuon pair; this ensures that relevant data is retained. As a check, a comparison between a new version of jTracker and Monte Carlo was made in order to see how accurately jTracker could reconstruct the events created by Monte Carlo. In this presentation, the results of the inquest and their potential effects on the programming will be shown. This work is supported by U.S. DOE MENP Grant DE-FG02-03ER41243.

  20. Monte Carlo dose mapping on deforming anatomy

    NASA Astrophysics Data System (ADS)

    Zhong, Hualiang; Siebers, Jeffrey V.

    2009-10-01

    This paper proposes a Monte Carlo-based energy and mass congruent mapping (EMCM) method to calculate the dose on deforming anatomy. Different from dose interpolation methods, EMCM separately maps each voxel's deposited energy and mass from a source image to a reference image with a displacement vector field (DVF) generated by deformable image registration (DIR). EMCM was compared with other dose mapping methods: energy-based dose interpolation (EBDI) and trilinear dose interpolation (TDI). These methods were implemented in EGSnrc/DOSXYZnrc, validated using a numerical deformable phantom and compared for clinical CT images. On the numerical phantom with an analytically invertible deformation map, EMCM mapped the dose exactly the same as its analytic solution, while EBDI and TDI had average dose errors of 2.5% and 6.0%. For a lung patient's IMRT treatment plan, EBDI and TDI differed from EMCM by 1.96% and 7.3% in the lung patient's entire dose region, respectively. As a 4D Monte Carlo dose calculation technique, EMCM is accurate and its speed is comparable to 3D Monte Carlo simulation. This method may serve as a valuable tool for accurate dose accumulation as well as for 4D dosimetry QA.

  1. Vertical and adiabatic excitations in anthracene from quantum Monte Carlo: Constrained energy minimization for structural and electronic excited-state properties in the JAGP ansatz

    SciTech Connect

    Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco Casula, Michele; Sorella, Sandro

    2015-06-07

    We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.

  2. Vertical and adiabatic excitations in anthracene from quantum Monte Carlo: Constrained energy minimization for structural and electronic excited-state properties in the JAGP ansatz.

    PubMed

    Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele

    2015-06-01

    We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account. PMID:26049481

  3. Effective one-body potential fitted for many-body interactions associated with a Jastrow function: application to the quantum Monte Carlo calculations

    NASA Astrophysics Data System (ADS)

    Umezawa, Naoto; Austin, Brian; Lester, William A., Jr.

    2009-03-01

    An efficient method of optimizing a Slater determinant, D, in the Jastrow-Slater-type wave function, FD, is suggested. Here, the so-called transcorrelated Hamiltonian, 1F H F, which is a similarity transformation of the usual Hamiltonian of an electronic system with respect to a Jastrow function F, is fitted to an effective Hamiltonian, Heff= ∑i^N ( -12 2̂i+ v(ri) ), in which all the electron-electron and electron-neucleus interactions are represented by a one-body potential, v(r). A single-particle Schr"odinger equation is then solved by using v(r) to determine the orbitals, of which the Slater determinant consists. The obtained orbitals improve the atomic total energies in the variational Monte Carlo calculations compared to those given by the density-functional-based orbitals. Advantages of using the optimized orbitals in the diffusion Monte Carlo calculations are also discussed.

  4. Dynamics of the Anderson model for dilute magnetic alloys: A quantum Monte Carlo and maximum entropy study

    SciTech Connect

    Silver, R.N.; Gubernatis, J.E.; Sivia, D.S. ); Jarrell, M. . Dept. of Physics)

    1990-01-01

    In this article we describe the results of a new method for calculating the dynamical properties of the Anderson model. QMC generates data about the Matsubara Green's functions in imaginary time. To obtain dynamical properties, one must analytically continue these data to real time. This is an extremely ill-posed inverse problem similar to the inversion of a Laplace transform from incomplete and noisy data. Our method is a general one, applicable to the calculation of dynamical properties from a wide variety of quantum simulations. We use Bayesian methods of statistical inference to determine the dynamical properties based on both the QMC data and any prior information we may have such as sum rules, symmetry, high frequency limits, etc. This provides a natural means of combining perturbation theory and numerical simulations in order to understand dynamical many-body problems. Specifically we use the well-established maximum entropy (ME) method for image reconstruction. We obtain the spectral density and transport coefficients over the entire range of model parameters accessible by QMC, with data having much larger statistical error than required by other proposed analytic continuation methods.

  5. Ab initio molecular dynamics with noisy and cheap quantum Monte Carlo forces: accurate calculation of vibrational frequencies

    NASA Astrophysics Data System (ADS)

    Luo, Ye; Sorella, Sandro

    2014-03-01

    We introduce a general and efficient method for the calculation of vibrational frequencies of electronic systems, ranging from molecules to solids. By performing damped molecular dynamics with ab initio forces, we show that quantum vibrational frequencies can be evaluated by diagonalizing the time averaged position-position or force-force correlation matrices, although the ionic motion is treated on the classical level within the Born-Oppenheimer approximation. The novelty of our approach is to evaluate atomic forces with QMC by means of a highly accurate and correlated variational wave function which is optimized simultaneously during the dynamics. QMC is an accurate and promising many-body technique for electronic structure calculation thanks to massively parallel computers. However, since infinite statistics is not feasible, property evaluation may be affected by large noise that is difficult to harness. Our approach controls the QMC stochastic bias systematically and gives very accurate results with moderate computational effort, namely even with noisy forces. We prove the accuracy and efficiency of our method on the water monomer[A. Zen et al., JCTC 9 (2013) 4332] and dimer. We are currently working on the challenging problem of simulating liquid water at ambient conditions.

  6. Quantum Monte Carlo study of a vortex in superfluid He4 and search for a vortex state in the solid

    NASA Astrophysics Data System (ADS)

    Galli, D. E.; Reatto, L.; Rossi, M.

    2014-06-01

    We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed He4 at zero temperature using the shadow path integral ground state method and the fixed phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid He4 at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius R and we find good agreement with the experimental value of the energy as a function of R without any free parameter. We have studied also He4 above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect He4 crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.

  7. Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene

    NASA Astrophysics Data System (ADS)

    Gour, Jeffrey R.; Piecuch, Piotr; Włoch, Marta

    2010-10-01

    The left-eigenstate completely renormalized (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as CR-EOMCC(2,3) [M. Włoch et al., Mol. Phys. 104, 2149 (2006); P. Piecuch et al., Int. J. Quantum Chem. 109, 3268 (2009)], and the companion ground-state CR-CC(2,3) methodology [P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005); P. Piecuch et al., Chem. Phys. Lett. 418, 467 (2006)] are used to determine the total electronic and adiabatic excitation energies corresponding to the ground and lowest three excited states of methylene. The emphasis is on comparing the CR-CC(2,3)/CR-EOMCC(2,3) results obtained with the large correlation-consistent basis sets of the aug-cc-pCV xZ (x = T, Q, 5) quality and the corresponding complete basis set (CBS) limits with the recently published variational and diffusion Quantum Monte Carlo (QMC) data [P. Zimmerman et al., J. Chem. Phys. 131, 124103 (2009)]. It is demonstrated that the CBS CR-CC(2,3)/CR-EOMCC(2,3) results are in very good agreement with the best QMC, i.e. diffusion MC (DMC) data, with errors in the total and adiabatic excitation energies of all calculated states on the order of a few millihartree and less than 0.1 eV, respectively, even for the challenging, strongly multi-reference C 1 A 1 state for which the basic EOMCC approach with singles and doubles completely fails. The agreement between the CBS CR-CC(2,3)/CR-EOMCC(2,3) and variational MC (VMC) results for the total energies is not as good as in the DMC case, but the excitation energies resulting from the CBS CR-CC(2,3)/CR-EOMCC(2,3) and VMC calculations agree very well.

  8. Implicit Monte Carlo diffusion - an acceleration method for Monte Carlo time dependent radiative transfer simulations

    SciTech Connect

    Gentile, N A

    2000-10-01

    We present a method for accelerating time dependent Monte Carlo radiative transfer calculations by using a discretization of the diffusion equation to calculate probabilities that are used to advance particles in regions with small mean free path. The method is demonstrated on problems with on 1 and 2 dimensional orthogonal grids. It results in decreases in run time of more than an order of magnitude on these problems, while producing answers with accuracy comparable to pure IMC simulations. We call the method Implicit Monte Carlo Diffusion, which we abbreviate IMD.

  9. A Wigner Monte Carlo approach to density functional theory

    NASA Astrophysics Data System (ADS)

    Sellier, J. M.; Dimov, I.

    2014-08-01

    In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn-Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales very well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn-Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.

  10. Four decades of implicit Monte Carlo

    DOE PAGESBeta

    Wollaber, Allan B.

    2016-04-25

    In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate formsmore » of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.« less

  11. Fission Matrix Capability for MCNP Monte Carlo

    SciTech Connect

    Carney, Sean E.; Brown, Forrest B.; Kiedrowski, Brian C.; Martin, William R.

    2012-09-05

    In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a

  12. A Monte Carlo approach to water management

    NASA Astrophysics Data System (ADS)

    Koutsoyiannis, D.

    2012-04-01

    Common methods for making optimal decisions in water management problems are insufficient. Linear programming methods are inappropriate because hydrosystems are nonlinear with respect to their dynamics, operation constraints and objectives. Dynamic programming methods are inappropriate because water management problems cannot be divided into sequential stages. Also, these deterministic methods cannot properly deal with the uncertainty of future conditions (inflows, demands, etc.). Even stochastic extensions of these methods (e.g. linear-quadratic-Gaussian control) necessitate such drastic oversimplifications of hydrosystems that may make the obtained results irrelevant to the real world problems. However, a Monte Carlo approach is feasible and can form a general methodology applicable to any type of hydrosystem. This methodology uses stochastic simulation to generate system inputs, either unconditional or conditioned on a prediction, if available, and represents the operation of the entire system through a simulation model as faithful as possible, without demanding a specific mathematical form that would imply oversimplifications. Such representation fully respects the physical constraints, while at the same time it evaluates the system operation constraints and objectives in probabilistic terms, and derives their distribution functions and statistics through Monte Carlo simulation. As the performance criteria of a hydrosystem operation will generally be highly nonlinear and highly nonconvex functions of the control variables, a second Monte Carlo procedure, implementing stochastic optimization, is necessary to optimize system performance and evaluate the control variables of the system. The latter is facilitated if the entire representation is parsimonious, i.e. if the number of control variables is kept at a minimum by involving a suitable system parameterization. The approach is illustrated through three examples for (a) a hypothetical system of two reservoirs

  13. Monte Carlo simulation of intercalated carbon nanotubes.

    PubMed

    Mykhailenko, Oleksiy; Matsui, Denis; Prylutskyy, Yuriy; Le Normand, Francois; Eklund, Peter; Scharff, Peter

    2007-01-01

    Monte Carlo simulations of the single- and double-walled carbon nanotubes (CNT) intercalated with different metals have been carried out. The interrelation between the length of a CNT, the number and type of metal atoms has also been established. This research is aimed at studying intercalated systems based on CNTs and d-metals such as Fe and Co. Factors influencing the stability of these composites have been determined theoretically by the Monte Carlo method with the Tersoff potential. The modeling of CNTs intercalated with metals by the Monte Carlo method has proved that there is a correlation between the length of a CNT and the number of endo-atoms of specific type. Thus, in the case of a metallic CNT (9,0) with length 17 bands (3.60 nm), in contrast to Co atoms, Fe atoms are extruded out of the CNT if the number of atoms in the CNT is not less than eight. Thus, this paper shows that a CNT of a certain size can be intercalated with no more than eight Fe atoms. The systems investigated are stabilized by coordination of 3d-atoms close to the CNT wall with a radius-vector of (0.18-0.20) nm. Another characteristic feature is that, within the temperature range of (400-700) K, small systems exhibit ground-state stabilization which is not characteristic of the higher ones. The behavior of Fe and Co endo-atoms between the walls of a double-walled carbon nanotube (DW CNT) is explained by a dominating van der Waals interaction between the Co atoms themselves, which is not true for the Fe atoms. PMID:17033783

  14. Status of Monte-Carlo Event Generators

    SciTech Connect

    Hoeche, Stefan; /SLAC

    2011-08-11

    Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically resorts to regarding events as factorized into different steps, ordered descending in the mass scales or invariant momentum transfers which are involved. In this picture, a hard interaction, described through fixed-order perturbation theory, is followed by multiple Bremsstrahlung emissions off initial- and final-state and, finally, by the hadronization process, which binds QCD partons into color-neutral hadrons. Each of these steps can be treated independently, which is the basic concept inherent to general-purpose event generators. Their development is nowadays often focused on an improved description of radiative corrections to hard processes through perturbative QCD. In this context, the concept of jets is introduced, which allows to relate sprays of hadronic particles in detectors to the partons in perturbation theory. In this talk, we briefly review recent progress on perturbative QCD in event generation. The main focus lies on the general-purpose Monte-Carlo programs HERWIG, PYTHIA and SHERPA, which will be the workhorses for LHC phenomenology. A detailed description of the physics models included in these generators can be found in [8]. We also discuss matrix-element generators, which provide the parton-level input for general-purpose Monte Carlo.

  15. Communication: Water on hexagonal boron nitride from diffusion Monte Carlo

    NASA Astrophysics Data System (ADS)

    Al-Hamdani, Yasmine S.; Ma, Ming; Alfè, Dario; von Lilienfeld, O. Anatole; Michaelides, Angelos

    2015-05-01

    Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of -84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.

  16. Communication: Water on hexagonal boron nitride from diffusion Monte Carlo

    SciTech Connect

    Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos; Alfè, Dario; Lilienfeld, O. Anatole von

    2015-05-14

    Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.

  17. Communication: Water on hexagonal boron nitride from diffusion Monte Carlo.

    PubMed

    Al-Hamdani, Yasmine S; Ma, Ming; Alfè, Dario; von Lilienfeld, O Anatole; Michaelides, Angelos

    2015-05-14

    Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of -84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT. PMID:25978876

  18. Positronic molecule calculations using Monte Carlo configuration interaction

    NASA Astrophysics Data System (ADS)

    Coe, Jeremy P.; Paterson, Martin J.

    2016-02-01

    We modify the Monte Carlo configuration interaction procedure to model atoms and molecules combined with a positron. We test this method with standard quantum chemistry basis sets on a number of positronic systems and compare results with the literature and full configuration interaction when appropriate. We consider positronium hydride, positronium hydroxide, lithium positride and a positron interacting with lithium, magnesium or lithium hydride. We demonstrate that we can capture much of the full configuration interaction results, but often require less than 10% of the configurations of these multireference wavefunctions. The effect of the number of frozen orbitals is also discussed.

  19. Monte Carlo procedure for protein design

    NASA Astrophysics Data System (ADS)

    Irbäck, Anders; Peterson, Carsten; Potthast, Frank; Sandelin, Erik

    1998-11-01

    A method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities rather than minimizing energy functions, is based upon a different and very efficient multisequence Monte Carlo scheme. By construction, the method ensures that the designed sequences represent good folders thermodynamically. A bootstrap procedure for the sequence space search is devised making very large chains feasible. The algorithm is successfully explored on the two-dimensional HP model [K. F. Lau and K. A. Dill, Macromolecules 32, 3986 (1989)] with chain lengths N=16, 18, and 32.

  20. Monte Carlo methods to calculate impact probabilities

    NASA Astrophysics Data System (ADS)

    Rickman, H.; Wiśniowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.

    2014-09-01

    Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward

  1. Monte Carlo radiation transport¶llelism

    SciTech Connect

    Cox, L. J.; Post, S. E.

    2002-01-01

    This talk summarizes the main aspects of the LANL ASCI Eolus project and its major unclassified code project, MCNP. The MCNP code provide a state-of-the-art Monte Carlo radiation transport to approximately 3000 users world-wide. Almost all hardware platforms are supported because we strictly adhere to the FORTRAN-90/95 standard. For parallel processing, MCNP uses a mixture of OpenMp combined with either MPI or PVM (shared and distributed memory). This talk summarizes our experiences on various platforms using MPI with and without OpenMP. These platforms include PC-Windows, Intel-LINUX, BlueMountain, Frost, ASCI-Q and others.

  2. Monte Carlo simulation for the transport beamline

    SciTech Connect

    Romano, F.; Cuttone, G.; Jia, S. B.; Varisano, A.; Attili, A.; Marchetto, F.; Russo, G.; Cirrone, G. A. P.; Schillaci, F.; Scuderi, V.; Carpinelli, M.

    2013-07-26

    In the framework of the ELIMED project, Monte Carlo (MC) simulations are widely used to study the physical transport of charged particles generated by laser-target interactions and to preliminarily evaluate fluence and dose distributions. An energy selection system and the experimental setup for the TARANIS laser facility in Belfast (UK) have been already simulated with the GEANT4 (GEometry ANd Tracking) MC toolkit. Preliminary results are reported here. Future developments are planned to implement a MC based 3D treatment planning in order to optimize shots number and dose delivery.

  3. Exascale Monte Carlo R&D

    SciTech Connect

    Marcus, Ryan C.

    2012-07-24

    Overview of this presentation is (1) Exascale computing - different technologies, getting there; (2) high-performance proof-of-concept MCMini - features and results; and (3) OpenCL toolkit - Oatmeal (OpenCL Automatic Memory Allocation Library) - purpose and features. Despite driver issues, OpenCL seems like a good, hardware agnostic tool. MCMini demonstrates the possibility for GPGPU-based Monte Carlo methods - it shows great scaling for HPC application and algorithmic equivalence. Oatmeal provides a flexible framework to aid in the development of scientific OpenCL codes.

  4. Modulated pulse bathymetric lidar Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Luo, Tao; Wang, Yabo; Wang, Rong; Du, Peng; Min, Xia

    2015-10-01

    A typical modulated pulse bathymetric lidar system is investigated by simulation using a modulated pulse lidar simulation system. In the simulation, the return signal is generated by Monte Carlo method with modulated pulse propagation model and processed by mathematical tools like cross-correlation and digital filter. Computer simulation results incorporating the modulation detection scheme reveal a significant suppression of the water backscattering signal and corresponding target contrast enhancement. More simulation experiments are performed with various modulation and reception variables to investigate the effect of them on the bathymetric system performance.

  5. A Monte Carlo algorithm for degenerate plasmas

    SciTech Connect

    Turrell, A.E. Sherlock, M.; Rose, S.J.

    2013-09-15

    A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.

  6. Monte Carlo simulation of the enantioseparation process

    NASA Astrophysics Data System (ADS)

    Bustos, V. A.; Acosta, G.; Gomez, M. R.; Pereyra, V. D.

    2012-09-01

    By means of Monte Carlo simulation, a study of enantioseparation by capillary electrophoresis has been carried out. A simplified system consisting of two enantiomers S (R) and a selector chiral C, which reacts with the enantiomers to form complexes RC (SC), has been considered. The dependence of Δμ (enantioseparation) with the concentration of chiral selector and with temperature have been analyzed by simulation. The effect of the binding constant and the charge of the complexes are also analyzed. The results are qualitatively satisfactory, despite the simplicity of the model.

  7. Kinetic Monte Carlo simulations of proton conductivity

    NASA Astrophysics Data System (ADS)

    Masłowski, T.; Drzewiński, A.; Ulner, J.; Wojtkiewicz, J.; Zdanowska-Frączek, M.; Nordlund, K.; Kuronen, A.

    2014-07-01

    The kinetic Monte Carlo method is used to model the dynamic properties of proton diffusion in anhydrous proton conductors. The results have been discussed with reference to a two-step process called the Grotthuss mechanism. There is a widespread belief that this mechanism is responsible for fast proton mobility. We showed in detail that the relative frequency of reorientation and diffusion processes is crucial for the conductivity. Moreover, the current dependence on proton concentration has been analyzed. In order to test our microscopic model the proton transport in polymer electrolyte membranes based on benzimidazole C7H6N2 molecules is studied.

  8. Monte Carlo analysis of magnetic aftereffect phenomena

    NASA Astrophysics Data System (ADS)

    Andrei, Petru; Stancu, Alexandru

    2006-04-01

    Magnetic aftereffect phenomena are analyzed by using the Monte Carlo technique. This technique has the advantage that it can be applied to any model of hysteresis. It is shown that a log t-type dependence of the magnetization can be qualitatively predicted even in the framework of hysteresis models with local history, such as the Jiles-Atherton model. These models are computationally much more efficient than the models with global history such as the Preisach model. Numerical results related to the decay of the magnetization as of function of time, as well as to the viscosity coefficient, are presented.

  9. Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations

    SciTech Connect

    Reboredo, F A; Hood, R Q; Kent, P C

    2009-01-06

    We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multi-determinant expansions of the trial wave function. The method can be generalized to other wave function forms such as pfaffians. We test the method in a model system where benchmark configuration interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77 245110 (2008)]. Tests of the method are

  10. Discrete diffusion Monte Carlo for frequency-dependent radiative transfer

    SciTech Connect

    Densmore, Jeffrey D; Kelly, Thompson G; Urbatish, Todd J

    2010-11-17

    Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique.

  11. Monte Carlo simulations within avalanche rescue

    NASA Astrophysics Data System (ADS)

    Reiweger, Ingrid; Genswein, Manuel; Schweizer, Jürg

    2016-04-01

    Refining concepts for avalanche rescue involves calculating suitable settings for rescue strategies such as an adequate probing depth for probe line searches or an optimal time for performing resuscitation for a recovered avalanche victim in case of additional burials. In the latter case, treatment decisions have to be made in the context of triage. However, given the low number of incidents it is rarely possible to derive quantitative criteria based on historical statistics in the context of evidence-based medicine. For these rare, but complex rescue scenarios, most of the associated concepts, theories, and processes involve a number of unknown "random" parameters which have to be estimated in order to calculate anything quantitatively. An obvious approach for incorporating a number of random variables and their distributions into a calculation is to perform a Monte Carlo (MC) simulation. We here present Monte Carlo simulations for calculating the most suitable probing depth for probe line searches depending on search area and an optimal resuscitation time in case of multiple avalanche burials. The MC approach reveals, e.g., new optimized values for the duration of resuscitation that differ from previous, mainly case-based assumptions.

  12. Multilevel Monte Carlo simulation of Coulomb collisions

    DOE PAGESBeta

    Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, R. E.; Cohen, B. I.

    2014-05-29

    We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε–2) or (ε–2(lnε)2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε–3) for direct simulation Monte Carlo or binary collision methods.more » We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10–5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.« less

  13. Multilevel Monte Carlo simulation of Coulomb collisions

    SciTech Connect

    Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, R. E.; Cohen, B. I.

    2014-05-29

    We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε–2) or (ε–2(lnε)2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε–3) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10–5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

  14. Composite biasing in Monte Carlo radiative transfer

    NASA Astrophysics Data System (ADS)

    Baes, Maarten; Gordon, Karl D.; Lunttila, Tuomas; Bianchi, Simone; Camps, Peter; Juvela, Mika; Kuiper, Rolf

    2016-05-01

    Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the specific problems that we consider: in simulations with composite path length stretching, high accuracy results are obtained even for simulations with modest numbers of photon packages, while simulations without biasing cannot reach convergence, even with a huge number of photon packages.

  15. Calculating Pi Using the Monte Carlo Method

    NASA Astrophysics Data System (ADS)

    Williamson, Timothy

    2013-11-01

    During the summer of 2012, I had the opportunity to participate in a research experience for teachers at the center for sustainable energy at Notre Dame University (RET @ cSEND) working with Professor John LoSecco on the problem of using antineutrino detection to accurately determine the fuel makeup and operating power of nuclear reactors. During full power operation, a reactor may produce 1021 antineutrinos per second with approximately 100 per day being detected. While becoming familiar with the design and operation of the detectors, and how total antineutrino flux could be obtained from such a small sample, I read about a simulation program called Monte Carlo. Further investigation led me to the Monte Carlo method page of Wikipedia2 where I saw an example of approximating pi using this simulation. Other examples where this method was applied were typically done with computer simulations2 or purely mathematical.3 It is my belief that this method may be easily related to the students by performing the simple activity of sprinkling rice on an arc drawn in a square. The activity that follows was inspired by those simulations and was used by my AP Physics class last year with very good results.

  16. THE MCNPX MONTE CARLO RADIATION TRANSPORT CODE

    SciTech Connect

    WATERS, LAURIE S.; MCKINNEY, GREGG W.; DURKEE, JOE W.; FENSIN, MICHAEL L.; JAMES, MICHAEL R.; JOHNS, RUSSELL C.; PELOWITZ, DENISE B.

    2007-01-10

    MCNPX (Monte Carlo N-Particle eXtended) is a general-purpose Monte Carlo radiation transport code with three-dimensional geometry and continuous-energy transport of 34 particles and light ions. It contains flexible source and tally options, interactive graphics, and support for both sequential and multi-processing computer platforms. MCNPX is based on MCNP4B, and has been upgraded to most MCNP5 capabilities. MCNP is a highly stable code tracking neutrons, photons and electrons, and using evaluated nuclear data libraries for low-energy interaction probabilities. MCNPX has extended this base to a comprehensive set of particles and light ions, with heavy ion transport in development. Models have been included to calculate interaction probabilities when libraries are not available. Recent additions focus on the time evolution of residual nuclei decay, allowing calculation of transmutation and delayed particle emission. MCNPX is now a code of great dynamic range, and the excellent neutronics capabilities allow new opportunities to simulate devices of interest to experimental particle physics; particularly calorimetry. This paper describes the capabilities of the current MCNPX version 2.6.C, and also discusses ongoing code development.

  17. Scalable Domain Decomposed Monte Carlo Particle Transport

    NASA Astrophysics Data System (ADS)

    O'Brien, Matthew Joseph

    In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation. The main algorithms we consider are: • Domain decomposition of constructive solid geometry: enables extremely large calculations in which the background geometry is too large to fit in the memory of a single computational node. • Load Balancing: keeps the workload per processor as even as possible so the calculation runs efficiently. • Global Particle Find: if particles are on the wrong processor, globally resolve their locations to the correct processor based on particle coordinate and background domain. • Visualizing constructive solid geometry, sourcing particles, deciding that particle streaming communication is completed and spatial redecomposition. These algorithms are some of the most important parallel algorithms required for domain decomposed Monte Carlo particle transport. We demonstrate that our previous algorithms were not scalable, prove that our new algorithms are scalable, and run some of the algorithms up to 2 million MPI processes on the Sequoia supercomputer.

  18. Discrete range clustering using Monte Carlo methods

    NASA Technical Reports Server (NTRS)

    Chatterji, G. B.; Sridhar, B.

    1993-01-01

    For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.

  19. Monte Carlo methods in lattice gauge theories

    SciTech Connect

    Otto, S.W.

    1983-01-01

    The mass of the O/sup +/ glueball for SU(2) gauge theory in 4 dimensions is calculated. This computation was done on a prototype parallel processor and the implementation of gauge theories on this system is described in detail. Using an action of the purely Wilson form (tract of plaquette in the fundamental representation), results with high statistics are obtained. These results are not consistent with scaling according to the continuum renormalization group. Using actions containing higher representations of the group, a search is made for one which is closer to the continuum limit. The choice is based upon the phase structure of these extended theories and also upon the Migdal-Kadanoff approximation to the renormalizaiton group on the lattice. The mass of the O/sup +/ glueball for this improved action is obtained and the mass divided by the square root of the string tension is a constant as the lattice spacing is varied. The other topic studied is the inclusion of dynamical fermions into Monte Carlo calculations via the pseudo fermion technique. Monte Carlo results obtained with this method are compared with those from an exact algorithm based on Gauss-Seidel inversion. First applied were the methods to the Schwinger model and SU(3) theory.

  20. Monte Carlo techniques for analyzing deep-penetration problems

    SciTech Connect

    Cramer, S.N.; Gonnord, J.; Hendricks, J.S.

    1986-02-01

    Current methods and difficulties in Monte Carlo deep-penetration calculations are reviewed, including statistical uncertainty and recent adjoint optimization of splitting, Russian roulette, and exponential transformation biasing. Other aspects of the random walk and estimation processes are covered, including the relatively new DXANG angular biasing technique. Specific items summarized are albedo scattering, Monte Carlo coupling techniques with discrete ordinates and other methods, adjoint solutions, and multigroup Monte Carlo. The topic of code-generated biasing parameters is presented, including the creation of adjoint importance functions from forward calculations. Finally, current and future work in the area of computer learning and artificial intelligence is discussed in connection with Monte Carlo applications.

  1. Monte Carlo modeling of spatial coherence: free-space diffraction.

    PubMed

    Fischer, David G; Prahl, Scott A; Duncan, Donald D

    2008-10-01

    We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335

  2. Quantum Monte Carlo calculations of magnetic moments and M1 transitions in $A\\leq7$ nuclei including meson-exchange currents

    SciTech Connect

    Marcucci, Laura; Pervin, Muslema; Pieper, Steven; Schiavilla, Rocco; Wiringa, Robert

    2008-12-01

    Green's function Monte Carlo calculations of magnetic moments and $M1$ transitions including two-body meson-exchange current (MEC) contributions are reported for $A\\leq7$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-2 three-nucleon potentials are used to generate the nuclear wave functions. The two-body meson-exchange operators are constructed to satisfy the continuity equation with the Argonne $v_{18}$ potential. The MEC contributions increase the $A$=3,7 isovector magnetic moments by 16\\% and the $A$=6,7 transition rates by 17--34\\%, bringing them into very good agreement with the experimental data.

  3. Radiation source modeling for Monte Carlo based treatment planning systems

    NASA Astrophysics Data System (ADS)

    Garnica Garza, Hector Mauricio

    In this study, we introduce a method to determine the energy spectrum delivered by a medical accelerator. The method relies on both Monte Carlo generated data and experimental measurements, but requires far fewer measurements than current attenuation-based methods, and much less information about the construction of the linear accelerator than full Monte Carlo based estimations, making it easy to perform in a clinical environment. The basic model used in this work makes use of the quantum absorption efficiency concept, which gives the probability that a photon of energy hn will deposit energy in a detector (film-screen detector in our case). Mathematically, our model is given by: M=Y0T dYhn dhn Eavghne hndhn where M is the absorbed energy in the film-screen detector, dYhn dhn is the photon spectrum, Eavghn is the average energy deposited per interacting photon, and ehn is the quantum absorption efficiency, and Y is the total photon fluence striking the detector. ehn and Eavghn were calculated by means of Monte Carlo simulation using the code MCNPX. The method works as follows: first, the primary photon fluence exiting the target is calculated from first principles by dividing the target into thin slabs (50--100mum) and adding the bremsstrahlung contribution from each slab. The electron fluence is calculated using the Phase Space Time Evolution Model, first proposed by Cordaro et al. and further refined by Huizenga et al. Ray tracing is used to attenuate the primary photon fluence as it passes through the flattening filter on its way to the detectors. Based on a detailed study of linear accelerator head scatter and of the known weaknesses of the Schiff cross-section we propose a multiplicative, energy-dependent empirical correction factor fa,hn=exp ahn to take into account the head scatter energy fluence, where a is a free parameter that is fixed by comparing the energy deposited in a screen-film detector irradiated by the spectrum in question to the theoretical

  4. Path integral Monte Carlo on a lattice. II. Bound states.

    PubMed

    O'Callaghan, Mark; Miller, Bruce N

    2016-07-01

    The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations. PMID:27575090

  5. Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins

    NASA Astrophysics Data System (ADS)

    Kulagin, S. A.; Prokof'ev, N.; Starykh, O. A.; Svistunov, B.; Varney, C. N.

    2013-02-01

    We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing—cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.

  6. Improved diffusion Monte Carlo and the Brownian fan

    NASA Astrophysics Data System (ADS)

    Weare, J.; Hairer, M.

    2012-12-01

    Diffusion Monte Carlo (DMC) is a workhorse of stochastic computing. It was invented forty years ago as the central component in a Monte Carlo technique for estimating various characteristics of quantum mechanical systems. Since then it has been used in applied in a huge number of fields, often as a central component in sequential Monte Carlo techniques (e.g. the particle filter). DMC computes averages of some underlying stochastic dynamics weighted by a functional of the path of the process. The weight functional could represent the potential term in a Feynman-Kac representation of a partial differential equation (as in quantum Monte Carlo) or it could represent the likelihood of a sequence of noisy observations of the underlying system (as in particle filtering). DMC alternates between an evolution step in which a collection of samples of the underlying system are evolved for some short time interval, and a branching step in which, according to the weight functional, some samples are copied and some samples are eliminated. Unfortunately for certain choices of the weight functional DMC fails to have a meaningful limit as one decreases the evolution time interval between branching steps. We propose a modification of the standard DMC algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the ``naive'' generalization of the standard algorithm would be impractical, due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation problem. We then provide a detailed heuristic explanation of why, in the case of rare event simulation, the new algorithm is expected to converge to a limiting process as the underlying stepsize goes to 0. This is shown

  7. Resist develop prediction by Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Sohn, Dong-Soo; Jeon, Kyoung-Ah; Sohn, Young-Soo; Oh, Hye-Keun

    2002-07-01

    Various resist develop models have been suggested to express the phenomena from the pioneering work of Dill's model in 1975 to the recent Shipley's enhanced notch model. The statistical Monte Carlo method can be applied to the process such as development and post exposure bake. The motions of developer during development process were traced by using this method. We have considered that the surface edge roughness of the resist depends on the weight percentage of protected and de-protected polymer in the resist. The results are well agreed with other papers. This study can be helpful for the developing of new photoresist and developer that can be used to pattern the device features smaller than 100 nm.

  8. Exploring theory space with Monte Carlo reweighting

    SciTech Connect

    Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun

    2014-10-13

    Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists and experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.

  9. Monte Carlo modeling and meteor showers

    NASA Technical Reports Server (NTRS)

    Kulikova, N. V.

    1987-01-01

    Prediction of short lived increases in the cosmic dust influx, the concentration in lower thermosphere of atoms and ions of meteor origin and the determination of the frequency of micrometeor impacts on spacecraft are all of scientific and practical interest and all require adequate models of meteor showers at an early stage of their existence. A Monte Carlo model of meteor matter ejection from a parent body at any point of space was worked out by other researchers. This scheme is described. According to the scheme, the formation of ten well known meteor streams was simulated and the possibility of genetic affinity of each of them with the most probable parent comet was analyzed. Some of the results are presented.

  10. Coherent scatter imaging Monte Carlo simulation.

    PubMed

    Hassan, Laila; MacDonald, Carolyn A

    2016-07-01

    Conventional mammography can suffer from poor contrast between healthy and cancerous tissues due to the small difference in attenuation properties. Coherent scatter slot scan imaging is an imaging technique which provides additional information and is compatible with conventional mammography. A Monte Carlo simulation of coherent scatter slot scan imaging was performed to assess its performance and provide system optimization. Coherent scatter could be exploited using a system similar to conventional slot scan mammography system with antiscatter grids tilted at the characteristic angle of cancerous tissues. System optimization was performed across several parameters, including source voltage, tilt angle, grid distances, grid ratio, and shielding geometry. The simulated carcinomas were detectable for tumors as small as 5 mm in diameter, so coherent scatter analysis using a wide-slot setup could be promising as an enhancement for screening mammography. Employing coherent scatter information simultaneously with conventional mammography could yield a conventional high spatial resolution image with additional coherent scatter information. PMID:27610397

  11. Green's function Monte Carlo in nuclear physics

    SciTech Connect

    Carlson, J.

    1990-01-01

    We review the status of Green's Function Monte Carlo (GFMC) methods as applied to problems in nuclear physics. New methods have been developed to handle the spin and isospin degrees of freedom that are a vital part of any realistic nuclear physics problem, whether at the level of quarks or nucleons. We discuss these methods and then summarize results obtained recently for light nuclei, including ground state energies, three-body forces, charge form factors and the coulomb sum. As an illustration of the applicability of GFMC to quark models, we also consider the possible existence of bound exotic multi-quark states within the framework of flux-tube quark models. 44 refs., 8 figs., 1 tab.

  12. Accuracy control in Monte Carlo radiative calculations

    NASA Technical Reports Server (NTRS)

    Almazan, P. Planas

    1993-01-01

    The general accuracy law that rules the Monte Carlo, ray-tracing algorithms used commonly for the calculation of the radiative entities in the thermal analysis of spacecraft are presented. These entities involve transfer of radiative energy either from a single source to a target (e.g., the configuration factors). or from several sources to a target (e.g., the absorbed heat fluxes). In fact, the former is just a particular case of the latter. The accuracy model is later applied to the calculation of some specific radiative entities. Furthermore, some issues related to the implementation of such a model in a software tool are discussed. Although only the relative error is considered through the discussion, similar results can be derived for the absolute error.

  13. MORSE Monte Carlo radiation transport code system

    SciTech Connect

    Emmett, M.B.

    1983-02-01

    This report is an addendum to the MORSE report, ORNL-4972, originally published in 1975. This addendum contains descriptions of several modifications to the MORSE Monte Carlo Code, replacement pages containing corrections, Part II of the report which was previously unpublished, and a new Table of Contents. The modifications include a Klein Nishina estimator for gamma rays. Use of such an estimator required changing the cross section routines to process pair production and Compton scattering cross sections directly from ENDF tapes and writing a new version of subroutine RELCOL. Another modification is the use of free form input for the SAMBO analysis data. This required changing subroutines SCORIN and adding new subroutine RFRE. References are updated, and errors in the original report have been corrected. (WHK)

  14. Exploring theory space with Monte Carlo reweighting

    DOE PAGESBeta

    Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun

    2014-10-13

    Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists andmore » experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less

  15. Monte Carlo modeling and meteor showers

    NASA Astrophysics Data System (ADS)

    Kulikova, N. V.

    1987-08-01

    Prediction of short lived increases in the cosmic dust influx, the concentration in lower thermosphere of atoms and ions of meteor origin and the determination of the frequency of micrometeor impacts on spacecraft are all of scientific and practical interest and all require adequate models of meteor showers at an early stage of their existence. A Monte Carlo model of meteor matter ejection from a parent body at any point of space was worked out by other researchers. This scheme is described. According to the scheme, the formation of ten well known meteor streams was simulated and the possibility of genetic affinity of each of them with the most probable parent comet was analyzed. Some of the results are presented.

  16. Angular biasing in implicit Monte-Carlo

    SciTech Connect

    Zimmerman, G.B.

    1994-10-20

    Calculations of indirect drive Inertial Confinement Fusion target experiments require an integrated approach in which laser irradiation and radiation transport in the hohlraum are solved simultaneously with the symmetry, implosion and burn of the fuel capsule. The Implicit Monte Carlo method has proved to be a valuable tool for the two dimensional radiation transport within the hohlraum, but the impact of statistical noise on the symmetric implosion of the small fuel capsule is difficult to overcome. We present an angular biasing technique in which an increased number of low weight photons are directed at the imploding capsule. For typical parameters this reduces the required computer time for an integrated calculation by a factor of 10. An additional factor of 5 can also be achieved by directing even smaller weight photons at the polar regions of the capsule where small mass zones are most sensitive to statistical noise.

  17. Monte Carlo simulations of medical imaging modalities

    SciTech Connect

    Estes, G.P.

    1998-09-01

    Because continuous-energy Monte Carlo radiation transport calculations can be nearly exact simulations of physical reality (within data limitations, geometric approximations, transport algorithms, etc.), it follows that one should be able to closely approximate the results of many experiments from first-principles computations. This line of reasoning has led to various MCNP studies that involve simulations of medical imaging modalities and other visualization methods such as radiography, Anger camera, computerized tomography (CT) scans, and SABRINA particle track visualization. It is the intent of this paper to summarize some of these imaging simulations in the hope of stimulating further work, especially as computer power increases. Improved interpretation and prediction of medical images should ultimately lead to enhanced medical treatments. It is also reasonable to assume that such computations could be used to design new or more effective imaging instruments.

  18. Monte-Carlo Simulation Balancing in Practice

    NASA Astrophysics Data System (ADS)

    Huang, Shih-Chieh; Coulom, Rémi; Lin, Shun-Shii

    Simulation balancing is a new technique to tune parameters of a playout policy for a Monte-Carlo game-playing program. So far, this algorithm had only been tested in a very artificial setting: it was limited to 5×5 and 6×6 Go, and required a stronger external program that served as a supervisor. In this paper, the effectiveness of simulation balancing is demonstrated in a more realistic setting. A state-of-the-art program, Erica, learned an improved playout policy on the 9×9 board, without requiring any external expert to provide position evaluations. The evaluations were collected by letting the program analyze positions by itself. The previous version of Erica learned pattern weights with the minorization-maximization algorithm. Thanks to simulation balancing, its playing strength was improved from a winning rate of 69% to 78% against Fuego 0.4.

  19. Monte Carlo simulations in Nuclear Medicine

    SciTech Connect

    Loudos, George K.

    2007-11-26

    Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.

  20. Monte Carlo simulations in Nuclear Medicine

    NASA Astrophysics Data System (ADS)

    Loudos, George K.

    2007-11-01

    Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.