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Sample records for j-j heisenberg model

  1. Evidence for an unconventional universality class from a two-dimensional dimerized quantum heisenberg model.

    PubMed

    Wenzel, Sandro; Bogacz, Leszek; Janke, Wolfhard

    2008-09-19

    The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

  2. Explaining the CMS e e j j and e pTj j excess and leptogenesis in superstring inspired E6 models

    NASA Astrophysics Data System (ADS)

    Dhuria, Mansi; Hati, Chandan; Rangarajan, Raghavan; Sarkar, Utpal

    2015-03-01

    We show that superstring-inspired E6 models can explain both the recently detected excess e e j j and e pTj j signals at CMS and also allow for leptogenesis. Working in an R -parity conserving, low-energy supersymmetric effective model, we show that the excess CMS events can be produced via the decay of exotic sleptons in Alternative Left-Right Symmetric Model of E6, which can also accommodate leptogenesis at a high scale. On the other hand, either the e e j j excess or the e pTj j excess can be produced via the decays of right-handed gauge bosons, but some of these scenarios may not accommodate letptogenesis as there will be strong B -L violation at low energy, which, along with the anomalous fast electroweak B +L violation, will wash out all baryon asymmetry. Baryogenesis below the electroweak scale may then need to be implemented in these models.

  3. A quantum fidelity study of the anisotropic next-nearest-neighbour triangular lattice Heisenberg model.

    PubMed

    Thesberg, Mischa; Sørensen, Erik S

    2014-10-22

    Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.

  4. Heisenberg necklace model in a magnetic field

    SciTech Connect

    Tsvelik, A. M.; Zaliznyak, I. A.

    2016-08-26

    Here, we study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We also consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I=3/2) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ~J1/3(γI)2/3, at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. Furthermore, this energy scale is insensitive to a magnetic field B. For μBB>Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2√+1.

  5. Heisenberg necklace model in a magnetic field

    DOE PAGES

    Tsvelik, A. M.; Zaliznyak, I. A.

    2016-08-26

    Here, we study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We also consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I=3/2) present on the same sites. We findmore » that the resulting necklace model has a characteristic energy scale, Λ~J1/3(γI)2/3, at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. Furthermore, this energy scale is insensitive to a magnetic field B. For μBB>Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2√+1.« less

  6. Heisenberg necklace model in a magnetic field

    NASA Astrophysics Data System (ADS)

    Tsvelik, A. M.; Zaliznyak, I. A.

    2016-08-01

    We study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J . We consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I =3 /2 ) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ ˜J1 /3(γI ) 2 /3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field B . For μBB >Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, √{2 }+1 .

  7. The XXZ Heisenberg model on random surfaces

    NASA Astrophysics Data System (ADS)

    Ambjørn, J.; Sedrakyan, A.

    2013-09-01

    We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

  8. Variational wave functions for the S =1/2 Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders

    NASA Astrophysics Data System (ADS)

    Ghorbani, Elaheh; Tocchio, Luca F.; Becca, Federico

    2016-02-01

    By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have superexchange couplings J and the third one has instead J'. This model interpolates between the square lattice and the isotropic triangular one, for J'/J ≤1 , and between the isotropic triangular lattice and a set of decoupled chains, for J /J'≤1 . We consider all the fully symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification (Zhou and Wen, arXiv:cond-mat/0210662) and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for J'/J ≤1 , the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., 0.7 ≲J'/J ≲0.8 . In contrast, for J /J'≤1 , a large spin-liquid region appears close to the limit of decoupled chains, i.e., for J /J'≲0.6 , while magnetically ordered phases with spiral order are stabilized close to the isotropic point.

  9. EDITORIAL: J J Thomson's Electron

    NASA Astrophysics Data System (ADS)

    Adams, Steve

    1997-07-01

    Westminster School, London, UK A few weeks ago David Thomson, J J Thomson's grandson, presented a Friday evening discourse at the Royal Institution. In it he traced the development of JJT's life from his early studies at Owen's College in Manchester, on to Trinity College Cambridge, his work under Rayleigh at the Cavendish, and his succession as Professor of Experimental Physics in 1884 (a post he passed on to Rutherford in 1919). These were years of heroic discoveries that shaped 20th century physics. Looking around the lecture theatre at all the bow-ties and dinner jackets, it must have been rather similar on 30 April 1897 when JJT delivered his famous discourse on 'Cathode Rays' in which he cautiously but confidently announced that his own results together with those of other experimenters (Lenard in particular):

    `....seem to favour the hypothesis that the carriers of the charges are smaller than the atoms of hydrogen.'
    In this issue articles by Leif Gerward and Christopher Cousins, and by Isobel Falconer explore the historical and philosophical context of that discovery. The sound-bites to history in many A-level courses have JJT as both the hero who single-handedly discovered the electron and the rather naive Victorian scientist who thought the atom was a plum pudding. It is valuable to see how Thomson's work pulled the threads of many experiments together and to realize that he may have been first to the post because of a difference in the philosophical approach to cathode rays in Britain compared to Europe. Experimental data must always be interpreted, and divergent philosophies can lead to quite different conclusions. The electron was, of course, the first subatomic particle to be identified. Christine Sutton's article looks at how 20th century discoveries reveal Nature's mysterious habit of repeating successful patterns---electrons for example have very close relations, the muon and the tau---but why? Perhaps the answer will come

  10. SU (N ) Heisenberg model with multicolumn representations

    NASA Astrophysics Data System (ADS)

    Okubo, Tsuyoshi; Harada, Kenji; Lou, Jie; Kawashima, Naoki

    2015-10-01

    The SU (N ) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at N =10 , indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for N ≥15 . This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

  11. Conserved Quantities in the Generalized Heisenberg Magnet (ghm) Model

    NASA Astrophysics Data System (ADS)

    Mushahid, N.; Hassan, M.; Saleem, U.

    2013-03-01

    We study the conserved quantities of the generalized Heisenberg magnet (GHM) model. We derive the nonlocal conserved quantities of the model using the iterative procedure of Brezin et al. [Phys. Lett. B82, 442 (1979).] We show that the nonlocal conserved quantities Poisson commute with local conserved quantities of the model.

  12. Néel temperature of quasi-low-dimensional Heisenberg antiferromagnets.

    PubMed

    Yasuda, C; Todo, S; Hukushima, K; Alet, F; Keller, M; Troyer, M; Takayama, H

    2005-06-03

    The Néel temperature T(N) of quasi-one- and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of interchain (interlayer) to intrachain (intralayer) coupling J(')/J down to J(')/J approximately = 10(-3). We find that T(N) obeys a modified random-phase approximationlike relation for small J(')/J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulas describing T(N) for a wide range of J(') and useful for the analysis of experimental measurements are presented.

  13. Quasideterminant solutions of the generalized Heisenberg magnet model

    NASA Astrophysics Data System (ADS)

    Saleem, U.; Hassan, M.

    2010-01-01

    In this paper we present the Darboux transformation for the generalized Heisenberg magnet (GHM) model based on the general linear Lie group GL(n) and construct multi-soliton solutions in terms of quasideterminants. Further we relate the quasideterminant multi-soliton solutions obtained by means of Darboux transformation with those obtained by the dressing method. We also discuss the model based on the Lie group SU(n) and obtain explicit soliton solutions of the model based on SU(2).

  14. Type-I integrable quantum impurities in the Heisenberg model

    NASA Astrophysics Data System (ADS)

    Doikou, Anastasia

    2013-12-01

    Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.

  15. Decay of transverse correlations in quantum Heisenberg models

    SciTech Connect

    Björnberg, Jakob E. E-mail: daniel@ueltschi.org; Ueltschi, Daniel E-mail: daniel@ueltschi.org

    2015-04-15

    We study a class of quantum spin systems that include the S=1/2 Heisenberg and XY-models and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random loop representations of the correlation functions, on stochastic domination and on first-passage percolation.

  16. Scaling behavior of the Heisenberg model in three dimensions.

    PubMed

    Gordillo-Guerrero, A; Kenna, R; Ruiz-Lorenzo, J J

    2013-12-01

    We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros, and confirm recent numerical estimates for critical exponents.

  17. J. J. Thomson goes to America.

    PubMed

    Downard, Kevin M

    2009-11-01

    Joseph John (J. J.) Thomson was an accomplished scientist who helped lay the foundations of nuclear physics. A humble man of working class roots, Thomson went on to become one of the most influential physicists of the late 19th century. He is credited with the discovery of the electron, received a Nobel Prize in physics in 1906 for investigations into the conduction of electricity by gases, was knighted in 1908, and served as a Cavendish Professor and Director of the laboratory for over 35 years from 1884. His laboratory attracted some of the world's brightest minds; Francis W. Aston, Niels H. D. Bohr, Hugh L. Callendar, Charles T. R. Wilson, Ernest Rutherford, George F. C. Searle, Geoffrey I. Taylor, and John S. E. Townsend all worked under him. This article recounts J. J. Thomson's visits to North America in 1896, 1903, 1909, and finally 1923. It presents his activities and his personal impressions of the people and society of the U.S.A. and Canada, and the science of atomic physics and chemistry in the late 1800s and early 1900s.

  18. Interpreting a CMS excess in l l j j +missing -transverse-momentum with the golden cascade of the minimal supersymmetric standard model

    NASA Astrophysics Data System (ADS)

    Allanach, Ben; Kvellestad, Anders; Raklev, Are

    2015-06-01

    The CMS experiment recently reported an excess consistent with an invariant mass edge in opposite-sign same flavor leptons, when produced in conjunction with at least two jets and missing transverse momentum. We provide an interpretation of the edge in terms of (anti)squark pair production followed by the "golden cascade" decay for one of the squarks: q ˜ →χ˜2 0q →l ˜ l q →χ˜1 0q l l in the minimal supersymmetric standard model. A simplified model involving binos, winos, an on-shell slepton, and the first two generations of squarks fits the event rate and the invariant mass edge. We check consistency with a recent ATLAS search in a similar region, finding that much of the good-fit parameter space is still allowed at the 95% confidence level (C.L.). However, a combination of other LHC searches, notably two-lepton stop pair searches and jets plus p T, rule out all of the remaining parameter space at the 95% C.L.

  19. A Symmetrized Basis for Transitions in the Heisenberg Model

    NASA Astrophysics Data System (ADS)

    Haydock, Roger; Nex, C. M. M.

    2013-03-01

    The spin-S Heisenberg model has 2S+1 states on each site, for which there are (2S+1)2 possible transitions between these states. For N sites there are (2S+1)N states and (2S+1)2N transitions between states. This rapid increase in the number of transitions with sites appears to limit calculations to just a few sites. However for transitions induced by spin-spin interactions, we construct a symmetrized basis which only grows as 2N-3, making possible computations for much larger systems. Supported by the Richmond F. Snyder Fund.

  20. Multipath Metropolis simulation: An application to the classical Heisenberg model

    NASA Astrophysics Data System (ADS)

    Rakić, Predrag S.; Radošević, Slobodan M.; Mali, Petar M.; Stričević, Lazar M.; Petrić, Tara D.

    2016-01-01

    This study explores the Multipath Metropolis simulation of the classical Heisenberg model. Unlike the standard single-path algorithm, the Metropolis algorithm applied to multiple random-walk paths becomes an embarrassingly parallel algorithm in which many processor cores can be easily utilized. This is important since processor cores are progressively becoming less expensive and thus more accessible. The most obvious advantage of the multipath approach is in employing independent random-walk paths to produce an uncorrelated simulation output with a normal distribution allowing for straightforward and rigorous statistical analysis.

  1. Ground states of the SU(N) Heisenberg model.

    PubMed

    Kawashima, Naoki; Tanabe, Yuta

    2007-02-02

    The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N> or =5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.

  2. Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model.

    PubMed

    He, Yin-Chen; Sheng, D N; Chen, Yan

    2014-04-04

    Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.

  3. Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model.

    PubMed

    Strecka, Jozef; Canová, Lucia; Minami, Kazuhiko

    2009-05-01

    The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.

  4. Exact Diagonalization of Heisenberg SU(N) models.

    PubMed

    Nataf, Pierre; Mila, Frédéric

    2014-09-19

    Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).

  5. Fractionalized Fermi liquid in a Kondo-Heisenberg model

    DOE PAGES

    Tsvelik, A. M.

    2016-10-10

    The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. Here, I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. The resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations, in agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003)]. Furthermore, the system undergoes amore » phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.« less

  6. Fractionalized Fermi liquid in a Kondo-Heisenberg model

    SciTech Connect

    Tsvelik, A. M.

    2016-10-10

    The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. Here, I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. The resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations, in agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003)]. Furthermore, the system undergoes a phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.

  7. Two Spin Liquid phases in the anisotropic triangular Heisenberg model

    NASA Astrophysics Data System (ADS)

    Sorella, Sandro

    2005-03-01

    Recently there have been rather clean experimental realizations of the quantum spin 1/2 Heisenberg Hamiltonian on a 2D triangular lattice geometry in systems like Cs2Cu Cl4 and organic compounds like k-(ET)2Cu2(CN)3. These materials are nearly two dimensional and are characterized by an anisotropic antiferromagnetic superexchange. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these interesting phenomena we have studied, by Quantum Monte Carlo methods, the triangular lattice Heisenberg model as a function of the strength of this anisotropy, represented by the ratio r between the intra-chain nearest neighbor coupling J' and the inter-chain one J. We have found evidence of two spin liquid regions, well represented by projected BCS wave functions[1,2] of the type proposed by P. W. Anderson at the early stages of High temperature superconductivity [3]. The first spin liquid phase is stable for small values of the coupling r 0.6 and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid, very similar to the one realized in the quantum dimer model in the triangular lattice[4]. It is characterized by a spin gap and a finite correlation length, and appears energetically favored in the region 0.6 r 0.9. The various phases are in good agreement with the experimental findings and supports the existence of spin liquid phases in 2D quantum spin-half systems. %%%%%%%%%%%%%%%%%% 1cm *[1] L. Capriotti F. Becca A. Parola and S. Sorella , Phys. Rev. Letters 87, 097201 (2001). *[2] S. Yunoki and S. Sorella Phys. Rev. Letters 92, 15003 (2004). *[3] P. W. Anderson, Science 235, 1186 (1987). *[4] P. Fendley, R. Moessner, and S. L. Sondhi Phys. Rev. B 66, 214513 (2002).

  8. Green function method study of the anisotropic ferromagnetic Heisenberg model on a square lattice

    NASA Astrophysics Data System (ADS)

    Hu, Ai-Yuan; Chen, Yuan

    2008-06-01

    We study the phase diagram of the anisotropic ferromagnetic Heisenberg model on a square lattice. We use the double-time Green’s function method within the Callen decoupling approximation. The dependence of the Curie temperature Tc on the spin S and on the anisotropy parameter Δ ( Δ=0 and 1 correspond to the isotropic Heisenberg and Ising model, respectively) is obtained explicitly. Our results are in agreement with results obtained from other theoretical approaches.

  9. Frustrated square lattice Heisenberg model and magnetism in Iron Telluride

    NASA Astrophysics Data System (ADS)

    Zaliznyak, Igor; Xu, Zhijun; Gu, Genda; Tranquada, John; Stone, Matthew

    2011-03-01

    We have measured spin excitations in iron telluride Fe1.1Te, the parent material of (1,1) family of iron-based superconductors. It has been recognized that J1-J2-J3 frustrated Heisenberg model on a square lattice might be relevant for the unusual magnetism and, perhaps, the superconductivity in cuprates [1,2]. Recent neutron scattering measurements show that similar frustrated model might also provide reasonable account for magnetic excitations in iron pnictide materials. We find that it also describes general features of spin excitations in FeTe parent compound observed in our recent neutron measurements, as well as in those by other groups. Results imply proximity of magnetic system to the limit of extreme frustration. Selection of spin ground state under such conditions could be driven by weak extrinsic interactions, such as lattice distortion, or strain. Consequently, different nonuniversal types of magnetic order could arise, both commensurate and incommensurate. These are not necessarily intrinsic to an ideal J1-J2-J3 model, but might result from lifting of its near degeneracy by weak extrinsic perturbations.

  10. Stapp's quantum dualism: The James and Heisenberg model of consciousness

    NASA Astrophysics Data System (ADS)

    Noyes, H. P.

    1994-02-01

    Henry Stapp attempts to resolve the Cartesian dilemma by introducing what the author would characterize as an ontological dualism between mind and matter. His model for mind comes from William James' description of conscious events and for matter from Werner Heisenberg's ontological model for quantum events (wave function collapse). His demonstration of the isomorphism between the two types of events is successful, but in the author's opinion fails to establish a monistic, scientific theory. The author traces Stapp's failure to his adamant rejection of arbitrariness, or 'randomness.' This makes it impossible for him (or for Bohr and Pauli before him) to understand the power of Darwin's explanation of biology, let alone the triumphs of modern 'neo-Darwinism.' The author notes that the point at issue is a modern version of the unresolved opposition between Leucippus and Democritus on one side and Epicurus on the other. Stapp's views are contrasted with recent discussions of consciousness by two eminent biologists: Crick and Edelman. They locate the problem firmly in the context of natural selection on the surface of the earth. Their approaches provide a sound basis for further scientific work. The author briefly examines the connection between this scientific (rather than ontological) framework and the new fundamental theory based on bit-strings and the combinatorial hierarchy.

  11. Universal stochastic series expansion algorithm for Heisenberg model and Bose-Hubbard model with interaction.

    PubMed

    Zyubin, M V; Kashurnikov, V A

    2004-03-01

    We propose a universal stochastic series expansion (SSE) method for the simulation of the Heisenberg model with arbitrary spin and the Bose-Hubbard model with interaction. We report the calculations involving soft-core bosons with interaction by the SSE method. Moreover, we develop a simple procedure for increased efficiency of the algorithm. From calculation of integrated autocorrelation times we conclude that the method is efficient for both models and essentially eliminates the critical slowing down problem.

  12. Fractional magnetization plateaus of the spin-1/2 Heisenberg orthogonal-dimer chain: Strong-coupling approach developed from the exactly solved Ising-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Verkholyak, Taras; Strečka, Jozef

    2016-10-01

    The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaus at zero, one-quarter, and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.

  13. Quantum phase diagrams and phase transitions in frustrated two-dimensional Heisenberg models

    NASA Astrophysics Data System (ADS)

    Sheng, Donna

    2014-03-01

    The quantum spin liquid is an emergent state of matter, which has attracted a lot of recent attention. I will review recent numerical progress based on the density matrix renormalization calculations in identifying gapped spin liquid in two-dimensional frustrated spin systems. I will first focus on extended model with Heisenberg exchange couplings on kagome lattice and demonstrate a topological state with fractionalized spinon and emergent gauge field clearly shown in numerical simulations. I will present concrete results on the quantum phase diagram of the extended kagome Heisenberg model, and compare that with the phase diagrams of the square and honeycomb lattice models with the dominant plaquette valence bond phase in nonmagnetic region. I will discuss numerical effort and theoretical challenge in fully pinning down the nature of the gapped topological phase, and also the nature of the quantum phase transitions in these Heisenberg systems. The research was supported by the National Science Foundation grant DMR-0906816.

  14. Cathode Ray Research Leading to J.J. Thomson's Discovery

    NASA Astrophysics Data System (ADS)

    Mulligan, Joseph

    1997-04-01

    This paper reviews the research on the properties and nature of cathode rays that led to the discovery of the electron by J. J. Thomson in the years 1897 - 1899. During the period from about 1870 to 1897 important research on cathode rays was carried out by William Crookes and Arthur Schuster in England, by Eugen Goldstein, Heinrich Hertz, Philipp Lenard, Emil Wiechert and Walter Kaufman in Germany, and by Jean Perrin in France. This research was always tedious and often inexact because fast vacuum pumps and convenient vacuum gauges did not yet exist. Still a few of these earlier researchers narrowly missed beating J. J. Thomson to the discover of the electron.

  15. High-temperature series expansion for spin-1/2 Heisenberg models

    NASA Astrophysics Data System (ADS)

    Hehn, Andreas; van Well, Natalija; Troyer, Matthias

    2017-03-01

    We present a high-temperature series expansion code for spin-1/2 Heisenberg models on arbitrary lattices. As an example we demonstrate how to use the application for an anisotropic triangular lattice with two independent couplings J1 and J2 and calculate the high-temperature series of the magnetic susceptibility and the static structure factor up to 12th and 10th order, respectively. We show how to extract effective coupling constants for the triangular Heisenberg model from experimental data on Cs2CuBr4.

  16. Monte Carlo simulation of Prussian blue analogs described by Heisenberg ternary alloy model

    NASA Astrophysics Data System (ADS)

    Yüksel, Yusuf

    2015-11-01

    Within the framework of Monte Carlo simulation technique, we simulate magnetic behavior of Prussian blue analogs based on Heisenberg ternary alloy model. We present phase diagrams in various parameter spaces, and we compare some of our results with those based on Ising counterparts. We clarify the variations of transition temperature and compensation phenomenon with mixing ratio of magnetic ions, exchange interactions, and exchange anisotropy in the present ferro-ferrimagnetic Heisenberg system. According to our results, thermal variation of the total magnetization curves may exhibit N, L, P, Q, R type behaviors based on the Néel classification scheme.

  17. Topological triple-vortex lattice stabilized by mixed frustration in expanded honeycomb Kitaev-Heisenberg model

    PubMed Central

    Yao, Xiaoyan; Dong, Shuai

    2016-01-01

    The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings. PMID:27229486

  18. Knight shifts around vacancies in the 2D Heisenberg model.

    PubMed

    Anfuso, Fabrizio; Eggert, Sebastian

    2006-01-13

    The local response to a uniform field around vacancies in the two-dimensional spin-1/2 Heisenberg antiferromagnet is determined by numerical quantum Monte Carlo simulations as a function of temperature. It is possible to separate the Knight shifts into uniform and staggered contributions on the lattice which are analyzed and understood in detail. The contributions show interesting long- and short-range behavior that may be of relevance in NMR and susceptibility measurements. For more than one impurity, remarkable nonlinear enhancement and cancellation effects take place. We predict that the Curie impurity susceptibility will be observable for a random impurity concentration even in the thermodynamic limit.

  19. Numerical evidence of spin-chirality decoupling in the three-dimensional heisenberg spin glass model.

    PubMed

    Viet, Dao Xuan; Kawamura, Hikaru

    2009-01-16

    Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG}>T_{SG}>0, exhibiting spin-chirality decoupling.

  20. Quantum phase transition, universality, and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on a honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Huang, Yi-Zhen; Xi, Bin; Chen, Xi; Li, Wei; Wang, Zheng-Chuan; Su, Gang

    2016-06-01

    The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J >0 in the armchair direction and ferromagnetic interaction J'<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q2 and spin stiffness ρ in two directions for various coupling ratios α =J'/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point αc=-0.93 . Through the finite-size scaling analysis on Q2, ρx, and ρy, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α . A phase diagram in the coupling ratio α -magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C (T ) for different α 's intersects precisely at one point, similar to that of liquid 3He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q2, ρ , and C (T ) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.

  1. Quantum phase transition, universality, and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on a honeycomb lattice.

    PubMed

    Huang, Yi-Zhen; Xi, Bin; Chen, Xi; Li, Wei; Wang, Zheng-Chuan; Su, Gang

    2016-06-01

    The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q_{2} and spin stiffness ρ in two directions for various coupling ratios α=J^{'}/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point α_{c}=-0.93. Through the finite-size scaling analysis on Q_{2}, ρ_{x}, and ρ_{y}, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T) for different α's intersects precisely at one point, similar to that of liquid ^{3}He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q_{2}, ρ, and C(T) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.

  2. Finite-temperature transition of the antiferromagnetic Heisenberg model on a distorted kagome lattice.

    PubMed

    Masuda, Hiroshi; Okubo, Tsuyoshi; Kawamura, Hikaru

    2012-08-03

    Motivated by the recent experiment on kagome-lattice antiferromagnets, we study the zero-field ordering behavior of the antiferromagnetic classical Heisenberg model on a uniaxially distorted kagome lattice by Monte Carlo simulations. A first-order transition, which has no counterpart in the corresponding undistorted model, takes place at a very low temperature. The origin of the transition is ascribed to a cooperative proliferation of topological excitations inherent to the model.

  3. Matrix model for strings beyond the c =1 barrier: The spin-s Heisenberg model on random surfaces

    NASA Astrophysics Data System (ADS)

    Ambjørn, J.; Khachatryan, Sh.; Sedrakyan, A.

    2015-07-01

    We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-s Heisenberg model on a regular 2d Manhattan lattice. Two-dimensional quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in noncritical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-s Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in the partition function to an integration over their eigenvalues.

  4. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  5. Spiral versus modulated collinear phases in the quantum axial next-nearest-neighbor Heisenberg model

    NASA Astrophysics Data System (ADS)

    Oitmaa, J.; Singh, R. R. P.

    2016-12-01

    Motivated by the discovery of spiral and modulated collinear phases in several magnetic materials, we investigate the magnetic properties of Heisenberg spin S =1 /2 antiferromagnets in two and three dimensions, with frustration arising from second-neighbor couplings in one axial direction [the axial next-nearest-neighbor Heisenberg (ANNNH) model]. Our results clearly demonstrate the presence of an incommensurate spiral phase at T =0 in two dimensions, extending to finite temperatures in three dimensions. The crossover between Néel and spiral order occurs at a value of the frustration parameter considerably above the classical value 0.25, a sign of substantial quantum fluctuations. We also investigate a possible modulated collinear phase with a wavelength of four lattice spacings and find that it has substantially higher energy and hence is not realized in the model.

  6. Second-order Peierls transition in the spin-orbital Kumar-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Brzezicki, Wojciech; Hagymási, Imre; Dziarmaga, Jacek; Legeza, Örs

    2015-05-01

    We add a Heisenberg interaction term ∝λ in the one-dimensional SU(2 )⊗XY spin-orbital model introduced by Kumar. At λ =0 the spin and orbital degrees of freedom can be separated by a unitary transformation leading to an exact solution of the model. We show that a finite λ >0 leads to spontaneous dimerization of the system which in the thermodynamic limit becomes a smooth phase transition at λ →0 , whereas it remains discontinuous within the first-order perturbation approach. We present the behavior of the entanglement entropy, energy gap, and dimerization order parameter in the limit of λ →0 confirming the critical behavior. Finally, we show the evidence of another phase transition in the Heisenberg limit, λ →∞ , and give a qualitative analytical explanation of the observed dimerized states both in the limit of small and large λ .

  7. Zigzag order and phase competition in expanded Kitaev-Heisenberg model on honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Yao, Xiaoyan

    2015-07-01

    The Kitaev-Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev-Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.

  8. Bicritical universality of the anisotropic Heisenberg model in a crystal field.

    PubMed

    Freire, R T S; Plascak, J A

    2015-03-01

    The bicritical properties of the three-dimensional classical anisotropic Heisenberg model in a crystal field are investigated through extensive Monte Carlo simulations on a simple cubic lattice, using Metropolis and Wolff algorithms. Field-mixing and multidimensional histogram techniques were employed in order to compute the probability distribution function of the extensive conjugate variables of interest and, using finite-size scaling analysis, the first-order transition line of the model was precisely located. The fourth-order cumulant of the order parameter was then calculated along this line and the bicritical point located with good precision from the cumulant crossings. The bicritical properties of this point were further investigated through the measurement of the universal probability distribution function of the order parameter. The results lead us to conclude that the studied bicritical point belongs in fact to the three-dimensional Heisenberg universality class.

  9. Triplet FFLO superconductivity in the doped Kitaev-Heisenberg honeycomb model

    NASA Astrophysics Data System (ADS)

    Liu, Tianhan; Repellin, Cécile; Douçot, Benoît; Regnault, Nicolas; Le Hur, Karyn

    2016-11-01

    We provide analytical and numerical evidence of spin-triplet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity in the itinerant Kitaev-Heisenberg model (antiferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of six inversion symmetry centers for the Fermi surface at nonzero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these nontrivial momenta, causing spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. Exact diagonalizations on finite clusters support this picture while ruling out a spin (charge) density wave.

  10. Role of Topological Defects in the Phase Transition of the Three-Dimensional Heisenberg Model.

    NASA Astrophysics Data System (ADS)

    Lau, Manhot

    The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a 'chemical potential' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to paramagnetic phase to occur. Such a conclusion is also consistent with a Renormalization Group study of the O(n) model, which suggests that topological defects should be explicitly taken into account for a correct description of the critical behavior in models including the three-dimensional Heisenberg model.

  11. Events Leading to J. J. Thomson's Electron in 1897

    NASA Astrophysics Data System (ADS)

    Dahl, Per F.

    1997-03-01

    The electron had its genesis in the glow discharge studies of the German school of Julius Plucker and company, who viewed their Kathodenstrahlen as a form of aetheral wave propagation. Next on the scene came the Victorian amateur scientists, personified by the incomparable William Crookes, who interpreted the rays in terms of material particulate behavior. Back on the Continent, meanwhile, there was Heinrich Hertz and his disciple Philipp Lenard--the latter with his metallic ``window'' and all it stood for. In England, an experimental rivalry ensued between J. J. Thomson and Arthur Schuster, who nearly beat ``J.J.'' to his corpuscle in 1890, while in Paris, about then, Jean Perrin's cathode ray studies were provoked by the lingering anti-atomic stance of his academic countrymen. The chronicle culminated in the charge-to-mass experiments of 1896-97, in which Emil Wiechert and Walter Kaufmann narrowly missed the electron in favor of Thomson and his classic e/m determinations.

  12. Variational study of the quantum phase transition in the bilayer Heisenberg model with bosonic RVB wavefunction.

    PubMed

    Liao, Haijun; Li, Tao

    2011-11-30

    We study the ground state phase diagram of the bilayer Heisenberg model on a square lattice with a bosonic resonating valence bond (RVB) wavefunction. The wavefunction has the form of a Gutzwiller projected Schwinger boson mean-field ground state and involves two variational parameters. We find the wavefunction provides an accurate description of the system on both sides of the quantum phase transition. In particular, through the analysis of the spin structure factor, ground state fidelity susceptibility and the Binder moment ratio Q(2), a continuous transition from the antiferromagnetic ordered state to the quantum disordered state is found at the critical coupling of α(c) = J(⊥)/J(∥) ≈ 2.62, in good agreement with the result of quantum Monte Carlo simulation. The critical exponent estimated from the finite size scaling analysis (1/ν ≈ 1.4) is consistent with that of the classical 3D Heisenberg universality class.

  13. Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Kos, Pavel; Punk, Matthias

    2017-01-01

    We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin S , we find three different symmetric Z2 spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops 120∘ order in the semiclassical limit at large S . In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.

  14. How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

    NASA Astrophysics Data System (ADS)

    De La Rosa Gomez, Alejandro; MacKay, Niall; Regelskis, Vidas

    2017-04-01

    We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl2 Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a ;bottom-up; approach for constructing integrable boundaries and can be applied to any spin chain model.

  15. a Matrix Model Representation of the Integrable Xxz Heisenberg Chain on Random Surfaces

    NASA Astrophysics Data System (ADS)

    Ambjørn, J.; Sedrakyan, A.

    2013-11-01

    We consider integrable models, i.e. models defined by R-matrices, on random Manhattan lattices (RML). The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. As an example we formulate a random matrix model where the partition function reproduces annealed average of the XXZ Heisenberg chain over all RML. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

  16. Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Scherer, Daniel D.; Scherer, Michael M.; Khaliullin, Giniyat; Honerkamp, Carsten; Rosenow, Bernd

    2014-07-01

    We study the quantum many-body instabilities of the t-JK-JH Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-1/2 model is believed to describe the magnetic properties of the layered transition-metal oxide Na2IrO3. We determine the ground state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow equations adapted to the lack of full spin-rotational invariance in the fermionic interactions, here represented by the highly frustrated and anisotropic Kitaev exchange term. Additionally employing a set of the Ward identities for the Kitaev-Heisenberg model, the numerical solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold (Z2 quantum spin liquids and magnetically ordered phases). We corroborate superconducting triplet p-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. For filling δ >1/4, the p-wave pairing gives rise to a topological state with protected Majorana edge modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchanges, we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice. Further, our flow equations are applicable to a wider class of model Hamiltonians.

  17. Random exchange interaction effects on the phase transitions in frustrated classical Heisenberg model

    SciTech Connect

    Li, W. C.; Song, X.; Feng, J. J.; Zeng, M.; Gao, X. S.; Qin, M. H.; Jia, X. T.

    2015-07-07

    In this work, the effects of the random exchange interaction on the phase transitions and phase diagrams of classical frustrated Heisenberg model are investigated by Monte Carlo simulation in order to simulate the chemical doping effect in real materials. It is observed that the antiferromagnetic transitions shift toward low temperature with the increasing magnitude of the random exchange interaction, which can be qualitatively understood from the competitions among local spin states. This study is related to the magnetic properties in the doped iron-based superconductors.

  18. Event-chain algorithm for the Heisenberg model: Evidence for z ≃1 dynamic scaling

    NASA Astrophysics Data System (ADS)

    Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

    2015-12-01

    We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z ≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z ≃2 .

  19. Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

    PubMed

    Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

    2015-12-01

    We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

  20. The Design of Control Pulses for Heisenberg Always-On Qubit Models

    NASA Astrophysics Data System (ADS)

    Magyar, Rudolph

    2015-03-01

    One model for a universal quantum computer is a spin array with constant nearest neighbor interactions and a controlled unidirectional site-specific magnetic field to generate unitary transformations. This system can be described by a Heisenberg spin Hamiltonian and can be simulated for on the order of 50 spins. It has recently been shown that time-dependent density functional inspired methods may be used to relate various spin models of qubits to ones that may be easier to compute numerically allowing potentially the efficient simulation of greater numbers of spins. One of the challenges of such an agenda is the identification of control pulses that produce desired gate operations (CNOT and single qubit phase gates). We apply control theory to design a universal set of pulses for a Heisenberg always-on model Hamiltonian for a few qubits and compare to known pulses when available. We suggest how this approach may be useful to design control pulses in other realistic designs. 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 Security Administration under contract DE-AC04-94AL85000.

  1. Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

    NASA Astrophysics Data System (ADS)

    Gotfryd, Dorota; Rusnačko, Juraj; Wohlfeld, Krzysztof; Jackeli, George; Chaloupka, Jiří; Oleś, Andrzej M.

    2017-01-01

    We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: Néel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.

  2. Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

    NASA Astrophysics Data System (ADS)

    Surungan, Tasrief; Zen, Freddy P.; Williams, Anthony G.

    2015-09-01

    Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in d-dimensional regular lattices for (d ≤ 3). We can make an analogy for the connectivity density (m) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of m for the existence of SG behaviour, analogous to the lower critical dimension (dl) for the canonical SG systems. Here we study system with m = 2, 3, 4 and 5. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of m and estimated its corersponding critical temperature.

  3. Stapp`s quantum dualism: The James/Heisenberg model of consciousness

    SciTech Connect

    Noyes, H.P.

    1994-02-18

    Henry Stapp attempts to resolve the Cartesian dilemma by introducing what the author would characterize as an ontological dualism between mind and matter. His model for mind comes from William James` description of conscious events and for matter from Werner Heisenberg`s ontological model for quantum events (wave function collapse). His demonstration of the isomorphism between the two types of events is successful, but in the author`s opinion fails to establish a monistic, scientific theory. The author traces Stapp`s failure to his adamant rejection of arbitrariness, or `randomness`. This makes it impossible for him (or for Bohr and Pauli before him) to understand the power of Darwin`s explanation of biology, let along the triumphs of modern `neo-Darwinism`. The author notes that the point at issue is a modern version of the unresolved opposition between Leucippus and Democritus on one side and Epicurus on the other. Stapp`s views are contrasted with recent discussions of consciousness by two eminent biologists: Crick and Edelman. They locate the problem firmly in the context of natural selection on the surface of the earth. Their approaches provide a sound basis for further scientific work. The author briefly examines the connection between this scientific (rather than ontological) framework and the new fundamental theory based on bit-strings and the combinatorial hierarchy.

  4. Quantum spin-1 anisotropic ferromagnetic Heisenberg model in a crystal field: a variational approach.

    PubMed

    Carvalho, D C; Plascak, J A; Castro, L M

    2013-09-01

    A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-1 anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature-dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still nonintegrable for quantum spin-1, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization, and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau-like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel, and Ising models, have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.

  5. Spontaneous plaquette dimerization in the J_1-J2 Heisenberg model

    NASA Astrophysics Data System (ADS)

    Capriotti, Luca; Sorella, Sandro

    2000-03-01

    The nature of the non magnetic phases of a quantum antiferromagnet is a topic of great interest and has been a subject of intense theoretical investigation since Anderson's suggestion [1] about the possible connections with the mechanism of high-Tc superconductivity. Within the Heisenberg model the simplest way in which the antiferromagnetism can be destabilized is by introducing a next-nearest-neighbor frustrating interaction leading to the so called J_1-J2 Hamiltonian. We have investigated the zero temperature properties the spin-half J_1-J2 Heisenberg antiferromagnet on the square lattice using exact diagonalization and the recently developed Green Function Monte Carlo with Stochastic Reconfiguration technique [2]. The spin gap and the susceptibilities for the most important crystal symmetry breaking operators have been computed. A genuine and somehow unexpected ``plaquette RVB'', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J_2/J1 ~= 0.5 [3]. ^1 P. W. Anderson, Science 235, 1196 (1987). ^2 S. Sorella, Phys. Rev. Lett. 80, 4558 (1998); S. Sorella and L. Capriotti, Phys. Rev. B (in press). ^3 L. Capriotti and S. Sorella, cond-mat/9911161

  6. Multicanonical Monte Carlo simulations of anisotropic SU(3) and SU(4) Heisenberg models

    NASA Astrophysics Data System (ADS)

    Harada, Kenji; Kawashima, Naoki; Troyer, Matthias

    2009-03-01

    We present the results of multicanonical Monte Carlo simulations on two-dimensional anisotropic SU(3) and SU(4) Heisenberg models. In our previous study [K. Harada, et al., J. Phys. Soc. Jpn. 76, 013703 (2007)], we found evidence for a direct quantum phase transition from the valence-bond-solid(VBS) phase to the SU(3) symmetry breaking phase on the SU(3) model and we proposed the possibility of deconfined critical phenomena (DCP) [T. Senthil, et al., Science 303, 1490 (2004); T. Grover and T. Senthil, Phys. Rev. Lett. 98, 247202 (2007)]. Here we will present new results with an improved algorithm, using a multicanonical Monte Carlo algorithm. Using a flow method-like technique [A.B. Kuklov, et al., Annals of Physics 321, 1602 (2006)], we discuss the possibility of DCP in both models.

  7. Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Nataf, Pierre; Lajkó, Miklós; Corboz, Philippe; Läuchli, Andreas M.; Penc, Karlo; Mila, Frédéric

    2016-05-01

    We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011), 10.1103/PhysRevA.84.011611]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.

  8. Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

    NASA Technical Reports Server (NTRS)

    Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy

    1989-01-01

    A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

  9. The replica symmetric solution for orthogonally constrained Heisenberg model on Bethe lattice

    NASA Astrophysics Data System (ADS)

    Concetti, Francesco

    2017-02-01

    In this paper, we study the thermodynamic properties of a system of D-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction J{{≤ft({{\\mathbf{S}}i}\\centerdot {{\\mathbf{S}}k}\\right)}2} . We can consider this model as a continuum version of anti-ferromagnetic D-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through the linear stability analysis, we obtain an instability line on the temperature-connectivity plane that provides a bound to the appearance of a phase transition. We also argue about the character of the instability observed.

  10. Exact ground state properties of the classical Heisenberg model for giant magnetic molecules

    SciTech Connect

    Axenovich, Maria; Luban, Marshall

    2001-03-01

    We find the exact ground state energy and magnetic moment for an arbitrary magnetic field H of the classical Heisenberg model of spins on the vertices of an icosidodecahedron. This model provides an accurate description of the magnetic properties of the giant paramagnetic molecule {l_brace}Mo{sub 72}Fe{sub 30}{r_brace} in which 30 Fe{sup 3+} ions are coupled via antiferromagnetic exchange. The strong frustration of the magnetic interaction in the molecule is relaxed when the angle between nearest-neighbor spins is 120{sup o}. We predict that the magnetic moment is linear with H until saturating at a critical field H{sub c}, and this is consistent with the results of a recent experiment at 0.46 K. We derive our results using a graph-theoretical construction and a special property, three-colorability, of the icosidodecahedron. We also consider spins on the vertices of an octahedron, icosahedron, and dodecahedron.

  11. Enhancing the Trace Norm and Bures Norm Measurement-Induced Nonlocality in the Heisenberg XYZ Model

    NASA Astrophysics Data System (ADS)

    Xie, Yu-Xia; Liu, Jing; Ma, Hong

    2016-11-01

    Nonlocality is one unique characteristic of quantum mechanics and an essential resource for quantum communication and computation. We investigate two measures of the well-defined geometric measurement-induced nonlocality (MIN) in the Heisenberg XYZ model, and found that considerable enhancement of the MINs can be achieved by tuning strength of the anisotropic parameter, the J z coupling, and the Dzyaloshinsky-Moriya (DM) interaction of the model. Particularly, the maxima of the two MINs can be obtained when the strength of the J z coupling or the DM interaction approaches infinity. We have also demonstrated the singular behaviors of the two MINs such as the nonunique states ordering and the sudden change behaviors.

  12. Effect of magnetic field on noncollinear magnetism in classical bilinear-biquadratic Heisenberg model

    NASA Astrophysics Data System (ADS)

    Pasrija, Kanika; Kumar, Sanjeev

    2016-05-01

    We present a Monte Carlo simulation study of a bilinear-biquadratic Heisenberg model on a two-dimensional square lattice in the presence of an external magnetic field. The study is motivated by the relevance of this simple model to the non-collinear magnetism and the consequent ferroelectric behavior in the recently discovered high-temperature multiferroic, cupric oxide (CuO). We show that an external magnetic field stabilizes a non-coplanar magnetic phase, which is characterized by a finite ferromagnetic moment along the direction of the applied magnetic field and a spiral spin texture if projected in the plane perpendicular to the magnetic field. Real-space analysis highlights a coexistence of non-collinear regions with ferromagnetic clusters. The results are also supported by simple variational calculations.

  13. Magnetic quantum phase transitions of the two-dimensional antiferromagnetic J1-J2 Heisenberg model

    NASA Astrophysics Data System (ADS)

    Cysne, T. P.; Silva Neto, M. B.

    2015-11-01

    We obtain the complete magnetic phase diagram of the two-dimensional antiferromagnetic J1\\text-J2 Heisenberg model, 0≤ α=J_2/J1≤1 , within the framework of the O(N) nonlinear sigma model. We find two magnetically ordered phases, one with Néel order, for α ≤ 0.4 , and another with collinear order, for α≥ 0.6 , separated by a nonmagnetic region, for 0.4≤ α ≤ 0.6 , where a gapped spin liquid is found. The transition at α=0.4 is of the second order while the one at α=0.6 is of the first order and the spin gaps cross at α=0.5 . Our results are exact at N → ∞ and agree with numerical results from different methods.

  14. Fermionology in the Kondo-Heisenberg model: the case of CeCoIn5

    NASA Astrophysics Data System (ADS)

    Zhong, Yin; Zhang, Lan; Lu, Han-Tao; Luo, Hong-Gang

    2015-09-01

    The Fermi surface of heavy electron systems plays a fundamental role in understanding their variety of puzzling phenomena, for example, quantum criticality, strange metal behavior, unconventional superconductivity and even enigmatic phases with yet unknown order parameters. The spectroscopy measurement of the typical heavy fermion superconductor CeCoIn5 has demonstrated multi-Fermi surface structure, which has not been studied in detail theoretically in a model system like the Kondo-Heisenberg model. In this work, we take a step toward such a theoretical model by revisiting the Kondo-Heisenberg model. It is found that the usual self-consistent calculation cannot reproduce the fermionology of the experimental observation of the system due to the sign binding between the hopping of the conduction electrons and the mean-field valence-bond order. To overcome such inconsistency, the mean-field valence-bond order is considered as a free/fitting parameter to correlate them with real-life experiments as performed in recent experiments [M.P. Allan, F. Massee, D.K. Morr, J. Van Dyke, A.W. Rost, A.P. Mackenzie, C. Petrovic, J.C. Davis, Nat. Phys. 9, 468 (2013); J. Van Dyke, F. Massee, M.P. Allan, J.C. Davis, C. Petrovic, D.K. Morr, Proc. Natl. Acad. Sci. 111, 11663 (2014)], which also explicitly reflects the intrinsic dispersion of local electrons observed in experimental measurements. Given the fermionology, the calculated effective mass enhancement, entropy, superfluid density and Knight shift are all in qualitative agreement with the experimental results of CeCoIn5, which confirms our assumption. Our result supports a d_{x^2 - y^2 }-wave pairing structure in the heavy fermion material CeCoIn5.

  15. Heisenberg's observability principle

    NASA Astrophysics Data System (ADS)

    Wolff, Johanna

    2014-02-01

    Werner Heisenberg's 1925 paper 'Quantum-theoretical re-interpretation of kinematic and mechanical relations' marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be 'founded exclusively upon relationships between quantities which in principle are observable'. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpretations of 'observability' along empiricist or positivist lines I argue that such readings are philosophically unsatisfying. Moreover, a careful comparison of Heisenberg's reinterpretation of classical kinematics with Einstein's argument against absolute simultaneity reveals that the positivist reading does not fit with Heisenberg's strategy in the paper. Instead the appeal to observability should be understood as a specific criticism of the causal inefficacy of orbital electron motion in Bohr's atomic model. I conclude that the tacit philosophical principle behind Heisenberg's argument is not a positivistic connection between observability and meaning, but the idea that a theory should not contain causally idle wheels.

  16. Spin excitations and thermodynamics of the antiferromagnetic Heisenberg model on the layered honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Vladimirov, Artem A.; Ihle, Dieter; Plakida, Nikolay M.

    2017-03-01

    We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, Néel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. The Néel temperature is calculated for arbitrary interlayer couplings. Our results are in a good agreement with numerical computations for finite clusters and with available experimental data on the β-Cu2V2O2 compound.

  17. Phase diagram of the classical Heisenberg model in a trimodal random field distribution

    NASA Astrophysics Data System (ADS)

    Santos-Filho, A.; Albuquerque, D. F. de; Santos-Filho, J. B.; Batista, T. S. Araujo

    2016-11-01

    The classical spin 1 / 2 Heisenberg model on a simple cubic lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated by effective field theory based on two-spin cluster. The random field is drawn from the asymmetric and anisotropic trimodal probability distribution. The fluctuating bond is extracted from the symmetric and anisotropic bimodal probability. We estimate the transition temperatures, and the phase diagram in the Tc- h, Tc- p and Tc - α planes. We observe that the temperature of the tricritical point decreases with the increase of disorder in exchange interactions until the system ceases to display tricritical behavior. The disorder of the interactions and reentrant phenomena depends on the trimodal distribution of the random field.

  18. Scaling of Entanglement Entropy for the Heisenberg Model on Clusters Joined by Point Contacts

    NASA Astrophysics Data System (ADS)

    Friedman, B. A.; Levine, G. C.

    2016-11-01

    The scaling of entanglement entropy for the nearest neighbor antiferromagnetic Heisenberg spin model is studied computationally for clusters joined by a single bond. Bisecting the balanced three legged Bethe cluster, gives a second Renyi entropy and the valence bond entropy which scales as the number of sites in the cluster. For the analogous situation with square clusters, i.e. two L × L clusters joined by a single bond, numerical results suggest that the second Renyi entropy and the valence bond entropy scales as L. For both systems, the environment and the system are connected by the single bond and interaction is short range. The entropy is not constant with system size as suggested by the area law.

  19. Effect of quantum phase transition on spin transport in the spatially frustrated Heisenberg model

    NASA Astrophysics Data System (ADS)

    Lima, L. S.

    2017-03-01

    We have used the Schwinger's boson theory to study the spin transport in the anisotropic two-dimensional spatially frustrated Heisenberg antiferromagnetic model in the square lattice. Our results show a sudden change in the AC spin conductivity σreg (ω) in the quantum phase transition point, where we have the gap of the system going to zero at critical point Dc=0. We have found a sudden change for a superconductor state in the DC limit ω → 0 independent of the value of the Drude's weight found in the quantum phase transition point. Away from it, we have obtained that the behavior of the spin conductivity changes for single peak at ω =ωp and in this case, σreg (ω) goes to zero in small ω and large ω limits.

  20. Comments on ""Lake Woebegone," Twenty Years Later" by J. J. Cannell, MD

    ERIC Educational Resources Information Center

    McRae, D. J.

    2006-01-01

    This article presents the author's comments on ""Lake Woebegone," Twenty Years Later" by J. J. Cannell, MD. J. J. Cannell's article on the so-called "Lake Woebegone" effect for K-12 educational testing systems is mostly an historical account of technical issues and policy considerations that led in part to development…

  1. EuCo2P2: A Model Molecular-Field Helical Heisenberg Antiferromagnet

    DOE PAGES

    Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; ...

    2016-07-19

    The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the ab plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ, high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperature T≤TNmore » with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. Additionally, the calculations also find ferromagnetic Eu–Eu exchange interactions within the ab plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χab(T≤TN).« less

  2. EuCo2P2 : A model molecular-field helical Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; Johnston, D. C.

    2016-07-01

    The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the a b plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ , high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperature T ≤TN with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ˜T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2 , respectively. These values are enhanced by a factor of ˜2.5 above those found from DFT electronic structure calculations for the two compounds. The calculations also find ferromagnetic Eu-Eu exchange interactions within the a b plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χa b(T ≤TN) .

  3. Honeycomb-Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals

    NASA Astrophysics Data System (ADS)

    Janssen, Lukas; Andrade, Eric C.; Vojta, Matthias

    2016-12-01

    The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A2IrO3 (A =Na , Li ) and α -RuCl3 . Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111 ] direction. We also discuss quantum corrections in the high-field phase.

  4. Honeycomb-Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals.

    PubMed

    Janssen, Lukas; Andrade, Eric C; Vojta, Matthias

    2016-12-30

    The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A_{2}IrO_{3} (A=Na, Li) and α-RuCl_{3}. Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.

  5. Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3.

    PubMed

    Chaloupka, Jirí; Jackeli, George; Khaliullin, Giniyat

    2010-07-09

    We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

  6. One-dimensional spin-1 ferromagnetic Heisenberg model with exchange anisotropy and single-ion anisotropy under external magnetic field

    NASA Astrophysics Data System (ADS)

    Song, Chuang-Chuang; Chen, Yuan; Liu, Ming-Wei

    2010-01-01

    The magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model are investigated by Green's function method. The magnetic properties of the system are treated by the random phase approximation for the exchange interaction term, and the Anderson-Callen approximation for the single-ion anisotropy term. The critical temperature, magnetization, and susceptibility are found to be dependent of the anisotropies. Our results are in agreement with the other theoretical results.

  7. Effects of a perpendicular magnetic field in the dipolar Heisenberg model with dominant exchange interaction.

    PubMed

    Abu-Labdeh, A M; MacIsaac, A B; De'Bell, K

    2011-07-27

    The effects of a uniform magnetic field on the phase diagram of the dipolar Heisenberg model with a dominant antiferromagnetic exchange interaction have been investigated. The model consists of a square lattice of classical spin vectors, where the spins interact through an antiferromagnetic exchange interaction of strength J and a dipole-dipole interaction of strength g. The spins couple to a magnetic surface anisotropy of strength κ and to an applied external magnetic field of strength H. The external field is applied perpendicular to the plane of the lattice. From extensive Monte Carlo simulations, representative magnetic phase diagrams have been determined as a function of the ratios κ/g and T/g, where T is temperature, and at three different ratios of H/g (H/g = 10, 20, 27). These results are compared to the previously investigated case of H/g = 0 and to analytic calculations for the ground state energies. The nature of the equilibrium phases and order of the phase boundaries separating them are considered and changes due to the strength of the applied field are highlighted.

  8. Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.

    PubMed

    Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan

    2012-06-27

    By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.

  9. Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain.

    PubMed

    Ananikian, N S; Ananikyan, L N; Chakhmakhchyan, L A; Rojas, Onofre

    2012-06-27

    The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.

  10. J. J. Sakurai Prize: Precision Quantum Chromodynamics at the LHC

    NASA Astrophysics Data System (ADS)

    Kosower, David

    2014-03-01

    The Large Hadron Collider (LHC) at CERN in Geneva, Switzerland, is the highest-energy particle collider operating today. In 2012, the two general-purpose detector collaborations, ATLAS and CMS, announced the discovery of the long-sought Higgs boson, the last missing particle of the Standard Model. The two collaborations have also set limits on new physics beyond the Standard Model, such as supersymmetry. Future direct and indirect searches for new physics require a precise, quantitative understanding of the known physics of the Standard Model, and in particular of the scattering of quark and gluon constituents of the proton under the strong force, known today as quantum chromodynamics (QCD). Achieving this level of understanding requires at least the incorporation of the first quantum corrections in perturbation theory - next-to-leading order (NLO) corrections - in scattering processes with several constituents leading to several jets in the final state. The new ``on-shell'' techniques, described earlier by Lance Dixon, have allowed these computations to be made beyond the reach of traditional diagrammatic methods. I will describe a direct numerical application of the new techniques in the BlackHat software library, and several phenomenological studies of physics at the LHC. These include studies relevant to CMS's supersymmetry searches, and to ATLAS measurements of electroweak vector-boson production with up to five associated jets. Partly supported by the European Research Council under Advanced Investigator Grant ERC-AdG-228301.

  11. Quantum correlation dynamics in a two-qubit Heisenberg XYZ model with decoherence

    NASA Astrophysics Data System (ADS)

    Yang, Guo-Hui; Zhang, Bing-Bing; Li, Lei

    2015-06-01

    Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord (QD). Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented: there is an “entanglement intermittently sudden death” phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter Δ. Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and Δ, whereas the parameter b is independent of the steady concurrence and QD. Project supported by the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2012021003-3) and the Special Funds of the National Natural Science Foundation of China (Grant No. 11247247).

  12. Pairing Symmetry of Heavy Fermion Superconductivity in the Two-Dimensional Kondo—Heisenberg Lattice Model

    NASA Astrophysics Data System (ADS)

    Liu, Yu; Zhang, Guang-Ming; Yu, Lu

    2014-08-01

    In the two-dimensional Kondo—Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion superconductivity. We find that the pairing symmetry strongly depends on the Fermi surface (FS) structure in the normal metallic state. When JH/JK is very small, the FS is a small hole-like circle around the corner of the Brillouin zone, and the s-wave pairing symmetry has a lower ground state energy. For the intermediate coupling values of JH/JK, the extended s-wave pairing symmetry gives the favored ground state. However, when JH/JK is larger than a critical value, the FS transforms into four small hole pockets crossing the boundary of the magnetic Brillouin zone, and the d-wave pairing symmetry becomes more favorable. In that regime, the resulting superconducting state is characterized by either a nodal d-wave or nodeless d-wave state, depending on the conduction electron filling factor as well. A continuous phase transition exists between these two states. This result may be related to the phase transition of the nodal d-wave state to a fully gapped state, which has recently been observed in Yb-doped CeCoIn5.

  13. Dynamical structure factors and excitation modes of the bilayer Heisenberg model

    NASA Astrophysics Data System (ADS)

    Lohöfer, M.; Coletta, T.; Joshi, D. G.; Assaad, F. F.; Vojta, M.; Wessel, S.; Mila, F.

    2015-12-01

    Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyze the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the low-energy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel, we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.

  14. Investigations of the Quantum Correlation in Two-Qubit Heisenberg XYZ Model with Decoherence

    NASA Astrophysics Data System (ADS)

    Guo-Hui, Yang

    2017-03-01

    Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated with the use of concurrence C and quantum discord (QD). With the Werner state as the initial state, we discuss the influence of mixture degree r on the dynamics. There are some difference between the time evolution behaviors of these two correlation measures with different value of r. For 0 ≤ r ≤ 1/3, there exists quantum discord but no entanglement; For 1/3< r<1, there is a "entanglement sudden death and birth" phenomenon in the concurrence but not in the QD; For r=1, there is one interesting thing that the concurrence decays from 1 to a minimum value close to 0 but the QD vanish. In addition, we have investigated the influence of different parameters on the two correlation measures. It has been found that, the concurrence and QD both exhibit osillatory behaviors with the time evolution, which is independent on the magnetic field B and the coupling coefficient J z . However, the Dzyaloshinskii-Moriya interaction (D) and coupling coefficient J have strong influence on concurrence and QD. With the increasing of the D or J, the frequency of the oscillation getting larger. When time is fixed, with the increasing of D or J, the concurrence and QD change periodically.

  15. Zero-temperature phase diagram of the classical Kane-Mele-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Zare, Mohammad H.; Fazileh, Farhad; Shahbazi, Farhad

    2013-06-01

    The classical phase diagram of the Kane-Mele-Heisenberg model is obtained using three complementary methods: Luttinger-Tisza, variational minimization, and the iterative minimization method. Six distinct phases were obtained in the space of the couplings. Three phases are commensurate with long-range ordering: planar Néel states in horizontal plane (phase I), planar states in the plane vertical to the horizontal plane (phase VI), and collinear states normal to the horizontal plane (phase II). However, the other three are infinitely degenerate due to the frustrating competition between the couplings, and they are characterized by a manifold of incommensurate wave vectors. These phases are planar helical states in a horizontal plane (phase III), planar helical states in a vertical plane (phase IV), and non-coplanar states (phase V). Employing the linear spin-wave analysis, it is found that the quantum fluctuations select a set of symmetrically equivalent states in phase III through the quantum order-by-disorder mechanism. Based on some heuristic arguments, it is argued that the same scenario may also occur in the other two frustrated phases VI and V.

  16. Monte Carlo simulations of intragrain spin effects in a quasi-2D Heisenberg model with uniaxial anisotropy.

    PubMed

    Leblanc, M D; Whitehead, J P; Plumer, M L

    2013-05-15

    A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J' and intergrain exchange J on the ordering temperature T(C) and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.

  17. Monte Carlo simulations of intragrain spin effects in a quasi-2D Heisenberg model with uniaxial anisotropy

    NASA Astrophysics Data System (ADS)

    Leblanc, M. D.; Whitehead, J. P.; Plumer, M. L.

    2013-05-01

    A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J‧ and intergrain exchange J on the ordering temperature TC and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.

  18. [Physiotherapy in metaphysial hip replacement with use J&J Proxima stem].

    PubMed

    Pasek, Jarosław; Koczy, Bodgan; Stołtny, Tomasz; Pajak, Jan; Pyda, Michał; Pasek, Tomasz; Kloza, Zygmunt; Sieroń, Aleksander

    2011-01-01

    In last years on the whole world violently grows up the number of patients at which occurrence productive degenerative changes of osteoarticular system. Actually these diseases more and more concern the young persons, active professionally. This consequences of these changes lead to limiting the functional functions of pond, pain as well as they worsen the quality of life. Pain in degenerative joint disease of various aetiology can be combated with the new surgical techniques offered by contemporary orthopaedics. Hip alloplasty is the only effective treatment method facilitating the restoration of physical fitness, correct mobility and the eradication of chronic pain. After operating introduces the different methods of improving finally. This work presents physiotherapeutic procedures, commenced on admission to the orthopaedic ward, involved in hip joint alloplasty with the J&J Proxima stem. The disseminating of introduced model of improving as well as the initiation him to program of the treatment confirms the legitimacy of choice, and it influences on improvement of the state of health also and the patients' functional efficiency with degenerative disease of hip joint.

  19. Comparison between spin restricted and unrestricted post-Hartree—Fock calculations of effective exchange integrals in Ising and Heisenberg models

    NASA Astrophysics Data System (ADS)

    Yamaguchi, K.; Okumura, M.; Mori, W.; Maki, J.; Takada, K.; Noro, T.; Tanaka, K.

    1993-07-01

    Spin-restricted and unrestricted post-Hartree—Fock calculations were carried out for clusters of triplet methylene and nitroxide radicals. The UHF-based methods such as UMP and QCISD followed by approximate spin projection provide reasonable energy differences between the high-and low-spin states of these species. They are close to the corresponding values from spin-restricted multi-reference (MR) approaches such as CASSCF and second-order (SO) CI. Implications of SOCI and MRSDCI results are discussed in relation to the size inconsistency erros involved in ab initio calculations of weak interaction energies, such as the effective exchange integrals in Ising and Heisenberg models.

  20. Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices.

    PubMed

    Strečka, Jozef; Ekiz, Cesur

    2015-05-01

    The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice.

  1. I Dream of J.J., or Affordances and Motion Pictures.

    ERIC Educational Resources Information Center

    Anderson, Joseph D.

    1995-01-01

    Categorizes attempts to account for how viewers garner meanings from motion pictures as either semiotic, realist, or conventionalist. Proposes an alternative explanation based on J. J. Gibson's ecological theory of perception. Offers his concept of "affordances" as the key to an explanation of how meanings in motion pictures are…

  2. Classification of magnons in rotated ferromagnetic Heisenberg model and their competing responses in transverse fields

    NASA Astrophysics Data System (ADS)

    Sun, Fadi; Ye, Jinwu; Liu, Wu-Ming

    2016-07-01

    In this paper, we study the rotated ferromagnetic Heisenberg model (RFHM) in two different transverse fields, hx and hz, which can be intuitively visualized as studying spin-orbit coupling (SOC) effects in two-dimensional (2D) Ising or anisotropic X Y model in a transverse field. At a special SOC class, it was found in our previous work [Phys. Rev. A 92, 043609 (2015), 10.1103/PhysRevA.92.043609] that the RFHM at a zero field owns an exact spin-orbit coupled ground state called the Y -x state. It supports not only the commensurate magnons (called C -C0 and C -Cπ ), but also the incommensurate magnons (called C-IC). These magnons are nonrelativistic, not embedded in the exact ground state, so need to be thermally excited or generated by various external probes. Their dramatic response under a longitudinal hy field was recently worked out by Sun et al. [arXiv:1502.05338]. Here we find they respond very differently under the two transverse fields. Any hx (hz) introduces quantum fluctuations to the ground state and changes the collinear Y -x state to a canted coplanar Y X -x (Y Z -x ) state. The C -C0,C -Cπ , and C-IC magnons become relativistic and sneak into the quantum ground state. We determine the competing boundaries among the C -C0,C -Cπ , and C-IC magnons, especially the detailed dispersions of the C-IC magnons inside the canted phases, which can be mapped out by the transverse spin structure factors. As hx (hz) increases further, the C -C0 magnons always win the competition and emerge as the seeds to drive a transition from the Y X -x (or Y Z -x ) to the ferromagnetic along the X (orZ ) direction called the X -FM (or Z -FM) phase. We show that the transition is in the 3D Ising universality class and it becomes the 3D X Y transition at the two Abelian points. We evaluate these magnons' contributions to magnetization and specific heat at low temperatures which can be measured by various established experimental techniques. The nature of the finite

  3. Magnetic properties, Lyapunov exponent and superstability of the spin-{1}/{2} Ising-Heisenberg model on a diamond chain

    NASA Astrophysics Data System (ADS)

    Ananikian, N.; Hovhannisyan, V.

    2013-05-01

    The exactly solvable spin-{1}/{2} Ising-Heisenberg model on a diamond chain has been considered. We have found the exact results for the magnetization using the recursion relation method. The existence of the magnetization plateau has been observed at one third of the saturation magnetization in the antiferromagnetic case. Some ground-state properties of the model are examined. At low temperatures, the system has two ferrimagnetic (FRI1 and FRI2) phases and one paramagnetic (PRM) phase. Lyapunov exponents for the various values of the exchange parameters and temperatures have been analyzed. It has also been shown that the maximal Lyapunov exponent exhibits plateau. Lyapunov exponents exhibit different behavior for two ferrimagnetic phases. We have found the existence of the supercritical point for the multi-dimensional rational mapping of the spin-{1}/{2} Ising-Heisenberg model on a diamond chain for the first time in the absence of the external magnetic field and T→0 in the antiferromagnetic case.

  4. Modified Heisenberg model for the zig-zag structure in multiferroic RMn{sub 2}O{sub 5}

    SciTech Connect

    Bahoosh, Safa Golrokh; Wesselinowa, Julia M.; Trimper, Steffen

    2015-08-28

    The class of RMn{sub 2}O{sub 5} (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn{sup 4+} and Mn{sup 3+} magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

  5. Model analysis of magnetic susceptibility of Sr2IrO4 : A two-dimensional Jeff=1/2 Heisenberg system with competing interlayer couplings

    NASA Astrophysics Data System (ADS)

    Takayama, Tomohiro; Matsumoto, Akiyo; Jackeli, George; Takagi, Hidenori

    2016-12-01

    We report the analysis of magnetic susceptibility χ (T ) of Sr2IrO4 single crystal in the paramagnetic phase. We formulate the theoretical susceptibility based on isotropic Heisenberg antiferromagnetism incorporating the Dzyaloshinsky-Moriya interaction exactly, and include the interlayer couplings in a mean-field approximation. χ (T ) above TN was found to be well described by the model, indicating the predominant Heisenberg exchange consistent with the microscopic theory. The analysis points to a competition of nearest and next-nearest-neighbor interlayer couplings, which results in the up-up-down-down configuration of the in-plane canting moments identified by the diffraction experiments.

  6. Anomalous spin excitation spectrum of the Heisenberg model in a magnetic field.

    PubMed

    Syljuåsen, Olav F; Lee, Patrick A

    2002-05-20

    Making the assumption that high-energy fermions exist in the two dimensional spin- 1/2 Heisenberg antiferromagnet, we present predictions based on the pi-flux ansatz for the dynamic structure factor when the antiferromagnet is subject to a uniform magnetic field. The main result is the presence of gapped excitations in a momentum region near (pi,pi) with energy lower than that at (pi,pi). This is qualitatively different from spin-wave theory predictions and may be tested by experiments or by quantum Monte Carlo.

  7. Spontaneous plaquette dimerization in the J1-J2 heisenberg model

    PubMed

    Capriotti; Sorella

    2000-04-03

    We investigate the nonmagnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected "plaquette resonating valence bond," with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J(2)/J(1) approximately 0.5.

  8. Interlayer-interaction dependence of latent heat in the Heisenberg model on a stacked triangular lattice with competing interactions.

    PubMed

    Tamura, Ryo; Tanaka, Shu

    2013-11-01

    We study the phase transition behavior of a frustrated Heisenberg model on a stacked triangular lattice by Monte Carlo simulations. The model has three types of interactions: the ferromagnetic nearest-neighbor interaction J(1) and antiferromagnetic third nearest-neighbor interaction J(3) in each triangular layer and the ferromagnetic interlayer interaction J([perpendicular]). Frustration comes from the intralayer interactions J(1) and J(3). We focus on the case that the order parameter space is SO(3)×C(3). We find that the model exhibits a first-order phase transition with breaking of the SO(3) and C(3) symmetries at finite temperature. We also discover that the transition temperature increases but the latent heat decreases as J([perpendicular])/J(1) increases, which is opposite to the behavior observed in typical unfrustrated three-dimensional systems.

  9. Berry phase in Heisenberg representation

    NASA Technical Reports Server (NTRS)

    Andreev, V. A.; Klimov, Andrei B.; Lerner, Peter B.

    1994-01-01

    We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.

  10. Chiral spin liquid and quantum criticality in extended S =1/2 Heisenberg models on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Wietek, Alexander; Läuchli, Andreas M.

    2017-01-01

    We investigate the J1-J2 Heisenberg model on the triangular lattice with an additional scalar chirality term and show that a chiral spin liquid is stabilized in a sizable region of the phase diagram. This topological phase is situated in between a coplanar 120∘ Néel ordered and a noncoplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the J1-J2 model. We compare the ground states from exact diagonalization with a Dirac spin liquid wave function and propose a scenario where this wave function describes the quantum critical point between the 120∘ magnetically ordered phase and a putative Z2 spin liquid.

  11. The magnetic properties of one-dimensional spin-1 ferromagnetic Heisenberg model in a magnetic field within Callen approximation

    NASA Astrophysics Data System (ADS)

    Liu, Ming-Wei; Chen, Yuan; Song, Chuang-Chuang; Wu, You; Ding, Hai-Ling

    2011-03-01

    The effect of magnetic field h on the magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model is studied by the double-time Green's function method. The magnetization and susceptibility are obtained within the Callen approximation. The zero-field susceptibility is as a decreasing function of the temperature T. The magnetization m increases in the whole field region, but the susceptibility maximum χ(Tm) decreases. The position Tm of the susceptibility maximum is both solved analytically and fits well to be a power law Tm∼hγ at low fields and to be linear increasing at high fields. The height χ(Tm) decreases as a power law χ(Tm)∼h with h increasing. The exponents (γ,β) obtained in our results agree with the other theoretical results. Our results are roughly in agreement with the results obtained in the experiment of Ni(OH)(NO3)H2O.

  12. Geometric Quantum Discord in the Heisenberg XX Model with Three-Spin Interactions

    NASA Astrophysics Data System (ADS)

    Xie, Yu-Xia; Liu, Jing; Sun, Yu-Hang

    2017-02-01

    Quantum discord is a resource for quantum information processing tasks, and seeking flexible ways to control it is of practical significance. We investigate the trace distance, Bures distance, and Hellinger distance geometric quantum discords (GQDs) for thermal states of the Heisenberg XX chain with three-spin interactions. The results show that both the XZX + YZY and XZY - YZX types of three-spin interactions can be used to enhance evidently the GQDs for the boundary spins of the chain. The optimal strengths of three-spin interactions for which the maximum enhancement of the GQDs are achieved are strongly dependent on the GQD measures we adopted and the number of spins in the chain.

  13. Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model

    NASA Astrophysics Data System (ADS)

    Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes

    2017-03-01

    We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.

  14. Strong anisotropy within a Heisenberg model in the Jeff=1/2 insulating state of Sr2Ir0.8Ru0.2O4

    NASA Astrophysics Data System (ADS)

    Calder, S.; Kim, J. W.; Taylor, A. E.; Upton, M. H.; Casa, D.; Cao, Guixin; Mandrus, D.; Lumsden, M. D.; Christianson, A. D.

    2016-12-01

    The dispersive magnetic excitations in Sr2IrO4 have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La2CuO4 . Here we investigate the inelastic spectra of Sr2Ir0.8Ru0.2O4 with resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr2IrO4 ; however, the disorder induced by the substitution of 20 %Ir4 + ions for Ru4 + removes longer range exchange interactions. A large spin gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due to the altered magnetic structure in Sr2Ir0.8Ru0.2O4 with c -axis aligned moments compared to the basal plane moments in the parent. Collectively the results indicate the robustness of a Heisenberg model description even when the magnetic structure is altered and the Jeff=1 /2 moments are diluted.

  15. Unconventional quantum ordered and disordered states in the highly frustrated spin-(1)/(2) Ising-Heisenberg model on triangles-in-triangles lattices

    NASA Astrophysics Data System (ADS)

    Čisárová, Jana; Strečka, Jozef

    2013-01-01

    The spin-(1)/(2) Ising-Heisenberg model on two geometrically related triangles-in-triangles lattices is exactly solved through the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the effective spin-(1)/(2) Ising model on a triangular lattice. Basic thermodynamic quantities were exactly calculated within this rigorous mapping method along with the ground-state and finite-temperature phase diagrams. Apart from the classical ferromagnetic phase, both investigated models exhibit several unconventional quantum ordered and disordered ground states. A mutual competition between two ferromagnetic interactions of basically different character generically leads to the emergence of a quantum ferromagnetic phase, in which a symmetric quantum superposition of three up-up-down states of the Heisenberg trimers accompanies a perfect alignment of all Ising spins. In the highly frustrated regime, we have either found the disordered quantum paramagnetic phase with a substantial residual entropy or a similar but spontaneously ordered phase with a nontrivial criticality at finite temperatures. The latter quantum ground state exhibits a striking coexistence of imperfect spontaneous order with partial disorder, which is evidenced by a quantum reduction of the spontaneous magnetization of Heisenberg spins that indirectly causes a small reduction of the spontaneous magnetization of otherwise classical Ising spins.

  16. Strong anisotropy within a Heisenberg model in the Jeff=12 insulating state of Sr2Ir0.8Ru0.2O4

    DOE PAGES

    Calder, Stuart A.; Kim, J. W.; Taylor, Alice E.; ...

    2016-12-28

    The dispersive magnetic excitations in Sr2IrO4 have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La2CuO4. In this paper, we investigate the inelastic spectra of Sr2Ir0.8Ru0.2O4 with resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr2IrO4; however, the disorder induced by the substitution of 20% Ir4+ ions for Ru4+ removes longer range exchange interactions. A large spin gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due tomore » the altered magnetic structure in Sr2Ir0.8Ru0.2O4 with c-axis aligned moments compared to the basal plane moments in the parent. Finally, collectively the results indicate the robustness of a Heisenberg model description even when the magnetic structure is altered and the Jeff = 1/2 moments are diluted.« less

  17. Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Si, Qimiao; Goswami, Pallab

    2014-03-01

    Heavy fermion systems represent a prototypical setting to study magnetic quantum phase transitions. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum non-linear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing dual orders of the antiferromagnetism, which can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Néel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo-singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy fermion systems at zero temperature. NSF.

  18. Classical O(N) Heisenberg model: Extended high-temperature series for two, three, and four dimensions

    NASA Astrophysics Data System (ADS)

    Butera, P.; Comi, M.; Marchesini, G.

    1990-06-01

    We present simple tables of integers from which it is possible to reconstruct the high-temperature series coefficients through β14 for the susceptibility, for the second correlation moment, and for the second field derivative of the susceptibility of the O(N) classical Heisenberg model on a simple (hyper)cubic lattice in dimension d=2, 3, and 4 and for any N. To construct the tables we have used the recent extension of the high-temperature series by M. Luscher and P. Weisz and some analytic properties in N that we have derived from the Schwinger-Dyson equations of the O(N) model. We also present a numerical study of these series in the d=2 case. The main results are: (a) the extended series give further support to the Cardy-Hamber-Nienhuis exact formulas for the critical exponents when -2=3 there are no indications of any critical point at finite β (c) the series are consistent with the low-temperature asymptotic forms predicted by the perturbative renormalization group.

  19. EuCo2P2: A Model Molecular-Field Helical Heisenberg Antiferromagnet

    SciTech Connect

    Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; Johnston, D. C.

    2016-07-19

    The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the ab plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ, high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperature T≤TN with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. Additionally, the calculations also find ferromagnetic Eu–Eu exchange interactions within the ab plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χab(T≤TN).

  20. Heat capacity and monogamy relations in the mixed-three-spin XXX Heisenberg model at low temperatures

    NASA Astrophysics Data System (ADS)

    Zad, Hamid Arian; Movahhedian, Hossein

    2016-08-01

    Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant J1 and spins (1/2,1/2) have coupling constant J2. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants J1 and J2. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.

  1. Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1 -J2 circle

    NASA Astrophysics Data System (ADS)

    Mikheyenkov, A. V.; Shvartsberg, A. V.; Valiulin, V. E.; Barabanov, A. F.

    2016-12-01

    Using the spherically symmetric self-consistent Green's function method, we consider thermodynamic properties of the S = 1 / 2J1 -J2 Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin-spin correlation functions cr = < S0z Srz >, the gaps in the spin excitation spectrum, the energy E and the heat capacity CV for the whole J1-J2-circle, i.e. for arbitrary φ, J1 = cos (φ), J2 = sin (φ). Due to low dimension there is no long-range order at T ≠ 0, but the short-range holds the memory of the parent zero-temperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(φ) and CV(φ) demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of cr(φ) lines have several nodes leading to nonmonotonic cr(T) dependence. For any fixed φ the heat capacity CV(T) always has maximum, tending to zero at T → 0, in the narrow vicinity of φ = 155 ° it exhibits an additional frustration-induced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at φ = 270 ° ± 0 and exponentially small antiferromagnetic gap up to (T ≲ 0.5) for φ ≳ 270 °.

  2. Investigation of Quantum Correlations for A S = 1/2 Ising-Heisenberg Model on a Symmetrical Diamond Chain

    NASA Astrophysics Data System (ADS)

    Faizi, E.; Eftekhari, H.

    2014-10-01

    We consider quantum correlations for a S = 1/2 Ising-Heisenberg model of a symmetrical diamond chain. First, we compare concurrence, quantum discord and 1-norm geometric quantum discord of an ideal diamond chain (Jm = 0) in the absence of magnetic field. The results show no simple ordering relations between these quantum correlations, so that quantum discord may be smaller or larger than the 1-norm geometric quantum discord, this observation contradicts the previous result provided by F. M. Paula [1]. Symmetrical behaviour of quantum correlation versus ferromagnetic and anti-ferromagnetic coupling constant J is considerable. The effect of external magnetic field B and temperature dependence is also considered. Furthermore, we study quantum discord and geometric measure of quantum discord with the effect of next nearest neighbour interaction between nodal Ising sites for a generalized diamond chain (Jm ≠ 0), and we observe coexistence of phases with different values of magnetic field for quantum correlations. Moreover, entanglement sudden death occurs while quantum discord, 1-norm geometric quantum discord and geometric measure of quantum discord are immune from sudden death.

  3. Phase transitions in a frustrated biquadratic Heisenberg model with coupled orbital degrees of freedom for iron-based superconductors

    NASA Astrophysics Data System (ADS)

    Zhuo, W. Z.; Qin, M. H.; Dong, S.; Li, X. G.; Liu, J.-M.

    2016-03-01

    In this paper, we study a biquadratic Heisenberg model with coupled orbital degrees of freedom by using a Monte Carlo simulation to investigate the phase transitions in iron-based superconductors. The antiferroquadrupolar state, which may be related to the magnetism of FeSe [R. Yu and Q. Si, Phys. Rev. Lett. 115, 116401 (2015), 10.1103/PhysRevLett.115.116401], is stabilized by the anisotropic biquadratic interaction induced by a ferro-orbital-ordered state. It is revealed that the orbital and nematic transitions occur at the same temperature for all the cases, supporting the mechanism of the orbital-driven nematicity as revealed in most recent experiments [S. H. Baek, D. V. Efremov, J. M. Ok, J. S. Kim, J. van den Brink, and B. Büchner, Nat. Mater. 14, 210 (2015), 10.1038/nmat4138]. In addition, it is suggested that the orbital interaction may lead to the separation of the structural and magnetic phase transitions, as observed in many families of iron pnictides.

  4. Multiple magnetization plateaus and magnetic structures in the S =1/2 Heisenberg model on the checkerboard lattice

    NASA Astrophysics Data System (ADS)

    Morita, Katsuhiro; Shibata, Naokazu

    2016-10-01

    We study the ground state of the S =1/2 Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at M /Msat=0 ,1/4 ,3/8 ,1/2 , and 3/4 , where Msat is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a 4 √{2 }×2 √{2 } magnetic unit cell with a 16-fold degeneracy.

  5. Heisenberg's First Paper

    ERIC Educational Resources Information Center

    Cassidy, David C.

    1978-01-01

    Describes some of the discussion, correspondances and assumptions of Heisenberg. Includes clarifying and defending his explanation of the anomalous Zeeman Effect to the Quantum Physicists of his time. (GA)

  6. Néel to spin-Peierls transition in a quasi-one-dimensional Heisenberg model coupled to bond phonons

    NASA Astrophysics Data System (ADS)

    Pillay, Jason Cornelius; Wierschem, Keola; Sengupta, Pinaki

    2013-08-01

    The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-(1)/(2) Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless Néel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the Néel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc shows a second order phase transition. The variation of the equilibrium bond length distortion δeq with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.

  7. Antiferromagnetic Heisenberg model on the icosahedron: influence of connectivity and the transition from the classical to the quantum limit.

    PubMed

    Konstantinidis, N P

    2015-02-25

    The antiferromagnetic Heisenberg model on the icosahedron presents unconventional properties at the classical and quantum level, which originate in the frustrated nature of the interactions between the spins. Here we examine the importance of the connectivity of the icosahedron for the appearance of a magnetization discontinuity as a function of an external field which separates two families of lowest energy configurations. We also investigate the transition from the classical to the quantum limit. The influence of connectivity on the magnetic properties is revealed by considering the cluster as being made up of a closed strip of a triangular lattice with two additional spins attached. The classical magnetization discontinuity is shown to evolve continuously from the discontinuity effected by these two spins when they are uncoupled to the cluster. In the second part the transition from the classical to the quantum limit is examined by focusing on the low energy spectrum, taking fully into account the spatial and the spin symmetry of the model in the characterization of the states. A symmetry analysis of the highly degenerate lowest energy classical manifold identifies as its direct fingerprint the low energy quantum states for spin magnitude as low as s = 1, with the latter following a tower of states behavior which relates to the icosahedron having a structure reminiscent of a depleted triangular lattice. The classical character of the AHM for small s is also detected on the ground state energy and correlation functions. On the other hand the classical magnetization discontinuity in a field eventually disappears for small s, after a weak reentrant behavior.

  8. The k-j-j' vector correlation in inelastic and reactive scattering

    NASA Astrophysics Data System (ADS)

    Brouard, M.; Chadwick, H.; Eyles, C. J.; Aoiz, F. J.; Kłos, J.

    2011-08-01

    Quasi-classical trajectory (QCT) methods are presented which allow characterization of the angular momentum depolarization of the products of inelastic and reactive scattering. The particular emphasis of the theory is on three-vector correlations, and on the connection with the two-vector correlation between the initial and final angular momenta, j and j^' }, which is amenable to experimental measurement. The formal classical theory is presented, and computational results for NO(A) + He are used to illustrate the type of mechanistic information provided by analysis of the two- and three-vector correlations. The classical j-j^' } two-vector correlation results are compared with quantum mechanical calculations, and are shown to be in good agreement. The data for NO(A) + He support previous conclusions [M. Brouard, H. Chadwick, Y.-P. Chang, R. Cireasa, C. J. Eyles, A. O. L. Via, N. Screen, F. J. Aoiz, and J. Kłos, J. Chem. Phys. 131, 104307 (2009)], 10.1063/1.3212608 that this system is only weakly depolarizing. Furthermore, it is shown that the projection of j along the kinematic apse is nearly conserved for this system under thermal collision energy conditions.

  9. The k-j-j' vector correlation in inelastic and reactive scattering.

    PubMed

    Brouard, M; Chadwick, H; Eyles, C J; Aoiz, F J; Kłos, J

    2011-08-28

    Quasi-classical trajectory (QCT) methods are presented which allow characterization of the angular momentum depolarization of the products of inelastic and reactive scattering. The particular emphasis of the theory is on three-vector correlations, and on the connection with the two-vector correlation between the initial and final angular momenta, j and j', which is amenable to experimental measurement. The formal classical theory is presented, and computational results for NO(A) + He are used to illustrate the type of mechanistic information provided by analysis of the two- and three-vector correlations. The classical j-j' two-vector correlation results are compared with quantum mechanical calculations, and are shown to be in good agreement. The data for NO(A) + He support previous conclusions [M. Brouard, H. Chadwick, Y.-P. Chang, R. Cireasa, C. J. Eyles, A. O. L. Via, N. Screen, F. J. Aoiz, and J. Kłos, J. Chem. Phys. 131, 104307 (2009)] that this system is only weakly depolarizing. Furthermore, it is shown that the projection of j along the kinematic apse is nearly conserved for this system under thermal collision energy conditions.

  10. Remarks towards the spectrum of the Heisenberg spin chain type models

    NASA Astrophysics Data System (ADS)

    Burdík, Č.; Fuksa, J.; Isaev, A. P.; Krivonos, S. O.; Navrátil, O.

    2015-05-01

    The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is considered. Finally, we discuss some questions relating to the general open Hecke chain models.

  11. In honour of Prof. Dr J.J.M. Franse. How to combine research, education and administration?

    NASA Astrophysics Data System (ADS)

    Brommer, P. E.

    2002-07-01

    On the occasion of the celebration of the 65th anniversary of Prof. Dr. J.J.M. Franse, a brief overview of his career and work is presented. His ability to combine fundamental research, educational tasks and administrative duties is emphasised.

  12. Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices.

    PubMed

    Tóth, Tamás A; Läuchli, Andreas M; Mila, Frédéric; Penc, Karlo

    2010-12-31

    Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.

  13. Novel local symmetries and chiral-symmetry-broken phases in S = 1/2 triangular-lattice Heisenberg model

    NASA Technical Reports Server (NTRS)

    Baskaran, G.

    1989-01-01

    Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.

  14. The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction

    NASA Astrophysics Data System (ADS)

    Zheng, Xiao; Zhang, Guo-Feng

    2017-01-01

    The effects of mixedness and entanglement on the lower bound and tightness of the entropic uncertainty in the Heisenberg model with Dzyaloshinski-Moriya (DM) interaction have been investigated. It is found that the mixedness can reflect the essence of the entropic uncertainty better than the entanglement. Meanwhile, the uncertainty of measurement results will be reduced by the entanglement and improved by the mixedness. The entanglement can destroy the tightness of the uncertainty, while the tightness will be improved with the increase in the mixedness. In addition, the tightness of the uncertainty in Heisenberg model can be expressed as a function of the magnetic properties, the strength of the DM interaction as well as the mixedness of the state and the functional form has no relationship with temperature. What's more, the entropic uncertain inequality becomes uncertain equality when the mixedness of the system reaches the minimum value. For a given mixedness, the tightness will be reduced with the increase in the strength of DM interaction at the antiferromagnetic case while the situation is just the opposite for the ferromagnetic case.

  15. The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation.

    PubMed

    Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G

    2009-07-02

    We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.

  16. Free Energy of the Three-Dimensional Spin-12 Quantum Heisenberg Model to O[T6

    NASA Astrophysics Data System (ADS)

    Chang, Chih-chun

    2001-11-01

    By applying the Friedberg-Lee-Ren's theorem (Ann. Phys. (N.Y.) 228, 52 (1993)) to the spin-12 three-dimensional isotropic quantum Heisenberg system, we obtain the low-temperature expansion of the free energy through a field theoretical calculation done in the equivalent lattice boson system. We reproduced Dyson's result and also extended it from T5 to T6. Nevertheless, because of the peculiar property of the spin operator being neither bosonic nor fermionic, the extension is not easy to obtain by other method.

  17. Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models

    NASA Astrophysics Data System (ADS)

    Kurita, Moyuru; Yamaji, Youhei; Morita, Satoshi; Imada, Masatoshi

    2015-07-01

    We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU(2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin

  18. Thermal entangled quantum Otto engine based on the two qubits Heisenberg model with Dzyaloshinskii-Moriya interaction in an external magnetic field

    NASA Astrophysics Data System (ADS)

    Wang, Hao; Wu, Guoxing; Chen, Daojiong

    2012-07-01

    Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii-Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.

  19. Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe.

    PubMed

    Yu, Rong; Si, Qimiao

    2015-09-11

    Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments.

  20. Stabilization of the chiral phase of the SU (6 m ) Heisenberg model on the honeycomb lattice with m particles per site for m larger than 1

    NASA Astrophysics Data System (ADS)

    Dufour, Jérôme; Mila, Frédéric

    2016-09-01

    We show that, when N is a multiple of 6 (N =6 m , where m is an integer), the SU (N) Heisenberg model on the honeycomb lattice with m particles per site has a clear tendency toward chiral order as soon as m ≥2 . This conclusion has been reached by a systematic variational Monte Carlo investigation of Gutzwiller projected wave functions as a function of m between the case of one particle per site (m =1 ), for which the ground state has recently been shown to be in a plaquette singlet state, and the m →∞ limit, where a mean-field approach has established that the ground state has chiral order. This demonstrates that the chiral phase can indeed be stabilized for not too large values of m , opening the way to its experimental realizations in other lattices.

  1. Antiferroquadrupolar and Ising-Nematic Orders of a Frustrated Bilinear-Biquadratic Heisenberg Model and Implications for the Magnetism of FeSe

    NASA Astrophysics Data System (ADS)

    Yu, Rong; Si, Qimiao

    2015-09-01

    Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments.

  2. Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions.

    PubMed

    Sandvik, Anders W

    2007-06-01

    Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

  3. Finite-Temperature Crossover Phenomenon in the S = 1/2 Antiferromagnetic Heisenberg Model on the Kagome Lattice

    NASA Astrophysics Data System (ADS)

    Shimokawa, Tokuro; Kawamura, Hikaru

    2016-11-01

    Thermal properties of the S = 1/2 kagome Heisenberg antiferromagnet at low temperatures are investigated by means of the Hams-de Raedt method for clusters of up to 36 sites possessing a full symmetry of the lattice. The specific heat exhibits, in addition to the double peaks, the third and the fourth peaks at lower temperatures. With decreasing the temperature, the type of the magnetic short-range order (SRO) changes around the third-peak temperature from the √{3} × √{3} to the q = 0 states, suggesting that the third peak of the specific heat is associated with a crossover phenomenon between the spin-liquid states with distinct magnetic SRO. Experimental implications are discussed.

  4. Fractionalized Z_{2} Classical Heisenberg Spin Liquids.

    PubMed

    Rehn, J; Sen, Arnab; Moessner, R

    2017-01-27

    Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.

  5. J. J. Sakurai Prize for Theoretical Particle Physics Talk: Collider Physics: Yesterday, Today and Tomorrow

    NASA Astrophysics Data System (ADS)

    Eichten, Estia

    2011-04-01

    More than a quarter century ago, theoretical issues with the Standard Model scalar boson sector inspired theorists to develop alternative models of electroweak symmetry breaking. The goal of the EHLQ study of hadron collider physics was to help determine the basic parameters of a supercollider that could distinguish these alternatives. Now we await data from the CMS and ATLAS experiments at CERN's Large Hadron Collider to solve this mystery. Does the Standard Model survive or, as theorists generally expect, does new physics appear (Strong Dynamics, SUSY, Extra Dimensions,...)? Even well into the LHC era it is likely that questions about the origin of fermion mass and mixings will remain and new physics will bring new puzzles. This time, the associated new scales are unknown. The opportunity to address new physics at a future multi-TeV lepton collider is briefly addressed.

  6. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2009-02-01

    Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

  7. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2011-09-01

    Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

  8. British American Tobacco ghost-wrote reports on tobacco advertising bans by the International Advertising Association and J J Boddewyn.

    PubMed

    Davis, R M

    2008-06-01

    In 1983 and 1986, the International Advertising Association (IAA) published an original version and then a revision of a report entitled "Tobacco Advertising Bans and Consumption in 16 Countries," which were edited by J J Boddewyn, a marketing professor. The reports concluded that tobacco advertising bans have not been accompanied by any significant reduction in tobacco consumption. Opponents of tobacco advertising restrictions trumpeted the IAA reports in print materials, media communications and legislative hearings during the 1980s and beyond. A new analysis of tobacco industry documents and transcripts of tobacco litigation testimony reveals that British American Tobacco ghost-wrote the IAA reports and that the Tobacco Institute (the trade association then representing the major US cigarette manufacturers) helped to arrange for Boddewyn to present the findings to the US Congress and the media. Further research on tobacco industry documents and tobacco litigation transcripts should assess whether tobacco industry sources were responsible for ghost-writing other studies favourable to the industry.

  9. J.J. Sakurai Prize for Theoretical Particle Physics: 40 Years of Lattice QCD

    NASA Astrophysics Data System (ADS)

    Lepage, Peter

    2016-03-01

    Lattice QCD was invented in 1973-74 by Ken Wilson, who passed away in 2013. This talk will describe the evolution of lattice QCD through the past 40 years with particular emphasis on its first years, and on the past decade, when lattice QCD simulations finally came of age. Thanks to theoretical breakthroughs in the late 1990s and early 2000s, lattice QCD simulations now produce the most accurate theoretical calculations in the history of strong-interaction physics. They play an essential role in high-precision experimental studies of physics within and beyond the Standard Model of Particle Physics. The talk will include a non-technical review of the conceptual ideas behind this revolutionary development in (highly) nonlinear quantum physics, together with a survey of its current impact on theoretical and experimental particle physics, and prospects for the future. Work supported by the National Science Foundation.

  10. Topological defects of Néel order and Kondo singlet formation for the Kondo-Heisenberg model on a honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Goswami, Pallab; Si, Qimiao

    2014-01-01

    Heavy-fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo-destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum nonlinear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing orders of the antiferromagnetism. We show that the antiferromagnetism and various competing singlet orders can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Néel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy-fermion systems at zero temperature.

  11. Heisenberg Model Analysis on Inelastic Powder Neutron Scattering Data Using Pure and K doped BaMn2 As2 samples

    NASA Astrophysics Data System (ADS)

    Ramazanoglu, Mehmet; Sapkota, A.; Pandey, A.; Johnston, D.; Goldman, Alan; Kreyssig, A.; Abernathy, D.; Niedziela, J.; Stone, M.; McQueeney, R. J.

    Low temperature powder inelastic neutron scattering measurements (INS) were performed on powders of Ba(1-x)KxMn2As2 with x=0(BMA),0.125 and 0.25. BMA is a G type antiferromagnet (AFM) which has local magnetic modulations bridging between the pnictide and cuprate superconductors. Hole doping (K) introduces more metallic behavior. The magnetic contribution to the intensities were retrieved by subtracting the estimated phonon background obtained at high momentum transfers from the raw. The resultant estimated magnetic intensities were analyzed by using damped harmonic oscillator model. The K doping effects create a broadening in the magnetic peak profiles consistent with expected weak FM fluctuations. We also analyzed the INS data using a powder integration routine which is based on J1-J2-Jz Heisenberg Model. The Monte Carlo integration technique is used to obtain the powder-averaged S(Q,E) for a series of Js. The representative values (with lowest chi-squared) obtained for BMA are in agreement with previous results. The values obtained for K doped samples were found in the close proximity to the parent ones. Overall we conclude that the original AFM structure seen in BMA retained its character even in the K doped samples with minimal differences. Work at Ames Laboratory is supported by USDOE under Contract No. DE-AC02-07CH11358 and Work at ITU is supported by TUBITAK 2232.

  12. Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m =2/3 magnetization

    NASA Astrophysics Data System (ADS)

    Kumar, Krishna; Changlani, Hitesh J.; Clark, Bryan K.; Fradkin, Eduardo

    2016-10-01

    We perform an exact-diagonalization study of the spin-1/2 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m =2/3 with an emphasis on the X Y point (Jz=0 ) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014), 10.1103/PhysRevB.90.174409] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σx y=1/2 . Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σx y=1/2 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

  13. Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

    NASA Astrophysics Data System (ADS)

    Arian Zad, Hamid

    2016-12-01

    We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J}1 and J}2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.

  14. The field-induced laws of thermodynamic properties in the two-dimensional spin-1 ferromagnetic Heisenberg model with the exchange and single-ion anisotropies

    NASA Astrophysics Data System (ADS)

    Pu, Qiurong; Chen, Yuan

    2013-02-01

    Green's function method is applied to investigate the two-dimensional spin-1 ferromagnetic Heisenberg model with the exchange and single-ion anisotropies. In the presence of the magnetic field, the effects of the anisotropies and field on the thermodynamic properties are obtained within the random phase approximation combining with Anderson-Callen approximation. The field-induced laws are found for the thermodynamic properties. Field dependences of heights of the susceptibility maximum and specific heat maximum fit well to power laws. The linear increase at high fields is shown for positions of the susceptibility maximum and specific heat maximum. A power law at low fields occurs for the position of the susceptibility maximum. At the positions of the maxima, the magnetization and internal energy display the power-law increase and linear decrease with the field, respectively. The exponents of the power laws are dependent of the anisotropies, as well as the slopes of the linear laws. Our results do not support the 2/3 power law which was obtained by the Landau theory.

  15. Cohomology of Heisenberg Lie superalgebras

    NASA Astrophysics Data System (ADS)

    Bai, Wei; Liu, Wende

    2017-02-01

    Suppose the ground field to be algebraically closed and of characteristic different from 2 and 3. All Heisenberg Lie superalgebras consist of two super-versions of the Heisenberg Lie algebras, 𝔥2m,n and 𝔟𝔞n with m a non-negative integer and n a positive integer. The space of a "classical" Heisenberg Lie superalgebra 𝔥2m,n is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super-analog of the Heisenberg Lie algebra, 𝔟𝔞n, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of 𝔥2m,n and 𝔟𝔞n with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In the characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structures for their cohomology. In the characteristic p > 3 case, we determine the associative superalgebra structure for the divided power cohomology of 𝔟𝔞n and we also make an attempt to determine the divided power cohomology of 𝔥2m,n by computing it in a low-dimensional case.

  16. Discrete flavour symmetries from the Heisenberg group

    NASA Astrophysics Data System (ADS)

    Floratos, E. G.; Leontaris, G. K.

    2016-04-01

    Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.

  17. Sub-Heisenberg phase uncertainties

    NASA Astrophysics Data System (ADS)

    Pezzé, Luca

    2013-12-01

    Phase shift estimation with uncertainty below the Heisenberg limit, ΔϕHL∝1/N¯T, where N¯T is the total average number of particles employed, is a mirage of linear quantum interferometry. Recently, Rivas and Luis, [New J. Phys.NJOPFM1367-263010.1088/1367-2630/14/9/093052 14, 093052 (2012)] proposed a scheme to achieve a phase uncertainty Δϕ∝1/N¯Tk, with k an arbitrary exponent. This sparked an intense debate in the literature which, ultimately, does not exclude the possibility to overcome ΔϕHL at specific phase values. Our numerical analysis of the Rivas and Luis proposal shows that sub-Heisenberg uncertainties are obtained only when the estimator is strongly biased. No violation of the Heisenberg limit is found after bias correction or when using a bias-free Bayesian analysis.

  18. Heisenberg and the critical mass

    NASA Astrophysics Data System (ADS)

    Bernstein, Jeremy

    2002-09-01

    An elementary treatment of the critical mass used in nuclear weapons is presented and applied to an analysis of the wartime activities of the German nuclear program. In particular, the work of Werner Heisenberg based on both wartime and postwar documents is discussed.

  19. Anti-anaphylactic effects of Trichilia monadelpha (Thonn.) J. J. De Wilde extracts on rodent models of anaphylaxis

    PubMed Central

    Ben, Inemesit Okon; Woode, Eric; Koffuor, George Asumeng; Asiamah, Emmanuel Akomanin

    2016-01-01

    Effects of petroleum ether and ethanolic extracts of Trichilia monadelpha stem bark (PEE and EAE) on compound 48/80-induced systemic and passive anaphylaxis were determined. Survival rate, extravasation, degranulation of mast cells, and secretion of tumour necrosis factor-α (TNF-α) and interleukin-6 (IL-6) were measured after pre-treatment with extracts (10-100 mg/kg) and disodium chromoglycate (2.5-250 μg/kg) and induction of anaphylaxis in C57BL/6 mice or Sprague-Dawley rats with compound 48/80. Histopathological assessments were made from skin biopsies of rats. Data was analyzed by Kaplan-Meier Survival Log-Rank Analysis, or One-way ANOVA and Holm-Sidak’s post hoc test. PEE and EAE inhibited (P ≤ 0.0001) tremors in systemic anaphylaxis passive cutaneous anaphylactic reactions and extravasation, stabilized or prevented (P ≤ 0.001-0.0001) mast cell degranulation, and inhibited (P ≤ 0.001-0.0001) TNF-α and IL-6 secretion. Per the findings, PEE and EAE of T. monadelpha have exhibited substantial anti-anaphylactic and anti-inflammatory property (with PEE performing better) which substantiates its use traditionally in management of allergies and other inflammatory disorders. PMID:27920822

  20. Chiral Kosterlitz-Thouless transition in the frustrated Heisenberg antiferromagnet on a pyrochlore slab.

    PubMed

    Kawamura, Hikaru; Arimori, Takuya

    2002-02-18

    Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally noncoplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.

  1. Conjugacy classes in discrete Heisenberg groups

    SciTech Connect

    Budylin, R Ya

    2014-08-01

    We study an extension of a discrete Heisenberg group coming from the theory of loop groups and find invariants of conjugacy classes in this group. In some cases, including the case of the integer Heisenberg group, we make these invariants more explicit. Bibliography: 4 titles.

  2. Integrability of Nonholonomic Heisenberg Type Systems

    NASA Astrophysics Data System (ADS)

    Grigoryev, Yury A.; Sozonov, Alexey P.; Tsiganov, Andrey V.

    2016-11-01

    We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical r-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.

  3. Holes in Heisenberg antiferromagnets

    NASA Astrophysics Data System (ADS)

    Chen, Yang

    1990-05-01

    In this Brief Report we show that a recent model proposed by Shankar [Phys. Rev. Lett. 63, 203 (1989)], describing the motion of holes in quantum antiferromagnets is equivalent to the Schwinger model [Phys. Rev. 128, 2425 (1962)] in 1+1 dimensions. Some exact results are deduced. In addition to the superconducting long-range order found by Shankar, it is shown that there is a 2pF hole density wave existing with the superconducting pairing instability.

  4. Evidence for a bicritical point in the XXZ Heisenberg antiferromagnet on a simple cubic lattice.

    PubMed

    Selke, Walter

    2011-04-01

    The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.

  5. Theory of disordered Heisenberg ferromagnets

    NASA Technical Reports Server (NTRS)

    Stubbs, R. M.

    1973-01-01

    A Green's function technique is used to calculate the magnetic properties of Heisenberg ferromagnets in which the exchange interactions deviate randomly in strength from the mean interaction. Systems of sc, bcc, and fcc topologies and of general spin values are treated. Disorder produces marked effects in the density of spin wave states, in the form of enhancement of the low-energy density and extension of the energy band to higher values. The spontaneous magnetization and the Curie temperature decrease with increasing disorder. The effects of disorder are shown to be more pronounced in the ferromagnetic than in the paramagnetic phase.

  6. Spin dynamics simulations for a nanoscale Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Hou, Zhuofei; Landau, D. P.; Brown, G.; Stocks, G. M.

    2010-03-01

    Thermoinduced magnetization(TiM) is a novel response which was predicted to occur in nanoscale antiferromagnetic materials. Extensive Monte Carlo simulations footnotetextG. Brown, A. Janotti, M. Eisenbach, and G. M. Stocks, Phys.Rev.B 72, 140405(2005) have shown that TiM is an intrinsic property of the antiferromagnetic classical Heisenberg model below the Neel temperature. To obtain a fundamental understanding of TiM, spin dynamics(SD) simulations are performed to study the spin wave behavior, which seems to be the cause of TiM. A classical Heisenberg model with an antiferromagnetic nearest-neighbor exchange interaction and uniaxial single-site anisotropy is studied. Simple-cubic lattices with free boundary conditions are used. We employed the fast spin dynamics algorithms with fourth-order Suzuki-Trotter decompositions of the exponential operator. Additional small excitation peaks due to surface effects are found in transverse S(q,w).

  7. Did Heisenberg Spit at Max Born?

    NASA Astrophysics Data System (ADS)

    Lustig, Harry

    2005-04-01

    In his 1985 book ``The Griffin,'' Arnold Kramish quotes an unnamed ``associate'' of Max Born that when Heisenberg ''was . . . a professor in Göttingen and when the Borns went to visit him, they were met with anti-Jewish sneers and obscenities, and in the end Heisenberg spat on the floor at Max Born's feet!". Kramish, in his own words, states that Heisenberg spat at Born and that the incident took place in 1933. Paul Lawrence Rose places the incident in 1953 and, on the basis of a fuller account from Kramish than the one published, identifies the associate as Born's secretary at Edinburgh University. One may be critical of Heisenberg's character and his behavior under the Nazis, and still be highly skeptical of the Kramish-Rose allegation. The life-long friendship between Born and Heisenberg and the respect which they displayed for each other before, during, and after the Nazi regime, has hardly been challenged by anyone. No known biography of Heisenberg mentions the alleged episode, and none of his obituaries alludes to it. There is no reference to it in Born's autobiography. None of the historians of science, German and American, whom I have consulted credit it. Although it is difficult to prove a negative, it is highly unlikely that Heisenberg spit at Born or on the floor on which they stood.

  8. 100 Years Werner Heisenberg: Works and Impact

    NASA Astrophysics Data System (ADS)

    Papenfuß, Dietrich; Lüst, Dieter; Schleich, Wolfgang P.

    2003-09-01

    Over 40 renowned scientists from all around the world discuss the work and influence of Werner Heisenberg. The papers result from the symposium held by the Alexander von Humboldt-Stiftung on the occasion of the 100th anniversary of Heisenberg's birth, one of the most important physicists of the 20th century and cofounder of modern-day quantum mechanics. Taking atomic and laser physics as their starting point, the scientists illustrate the impact of Heisenberg's theories on astroparticle physics, high-energy physics and string theory right up to processing quantum information.

  9. Heisenberg picture approach to the stability of quantum Markov systems

    SciTech Connect

    Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.

    2014-06-15

    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

  10. Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.

    PubMed

    Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R

    2016-05-13

    The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

  11. Werner Heisenberg (1901-1976)

    NASA Astrophysics Data System (ADS)

    Yang, Chen Ning

    2013-05-01

    Werner Heisenberg was one of the greatest physicists of all times. When he started out as a young research worker, the world of physics was in a very confused and frustrating state, which Abraham Pais has described1 as: It was the spring of hope, it was the winter of despair using Charles Dickens' words in A Tale of Two Cities. People were playing a guessing game: There were from time to time great triumphs in proposing, through sheer intuition, make-shift schemes that amazingly explained some regularities in spectral physics, leading to joy. But invariably such successes would be followed by further work which reveal the inconsistency or inadequacy of the new scheme, leading to despair...

  12. Adiabatic limits on Riemannian Heisenberg manifolds

    SciTech Connect

    Yakovlev, A A

    2008-02-28

    An asymptotic formula is obtained for the distribution function of the spectrum of the Laplace operator, in the adiabatic limit for the foliation defined by the orbits of an invariant flow on a compact Riemannian Heisenberg manifold. Bibliography: 21 titles.

  13. Scaling beyond CMOS: Turing-Heisenberg Rapprochement

    NASA Astrophysics Data System (ADS)

    Zhirnov, Victor V.; Cavin, Ralph K., III

    2010-09-01

    The primary objective of this study is to explore the connection of the device physics in the Boltzmann-Heisenberg limits and the parameters of the digital circuits implemented from these devices. We offer an abstraction of a Minimal Turing Machine built from the limiting devices and circuits, thus Turing-Heisenberg Rapprochement. The analysis suggests a possible limit to computational performance similar to the Carnot efficiency limit for heat engines.

  14. Effective low-energy description of almost Ising-Heisenberg diamond chain

    NASA Astrophysics Data System (ADS)

    Derzhko, Oleg; Krupnitska, Olesia; Lisnyi, Bohdan; Strečka, Jozef

    2015-11-01

    We consider a geometrically frustrated spin-(1/2) Ising-Heisenberg diamond chain, which is an exactly solvable model when assuming part of the exchange interactions as Heisenberg ones and another part as Ising ones. A small XY part is afterwards perturbatively added to the Ising couplings, which enabled us to derive an effective Hamiltonian describing the low-energy behavior of the modified but full quantum version of the initial model. The effective model is much simpler and free of frustration. It is shown that the XY part added to the originally Ising interaction gives rise to the spin-liquid phase with continuously varying magnetization, which emerges between the magnetization plateaus and is totally absent in the initial hybrid diamond-chain model. The elaborated approach can also be applied to other hybrid Ising-Heisenberg spin systems.

  15. Open timelike curves violate Heisenberg's uncertainty principle.

    PubMed

    Pienaar, J L; Ralph, T C; Myers, C R

    2013-02-08

    Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity.

  16. The Human Mind As General Problem Solver, Is Observed To Find ``Best'' Solutions, That Correspond To Highest Mental Coherence: Will Discuss ``sing Glass Type Theory'' of Princeton Physicist J J Hopfield, Points To How Best Use Our Own Human Mind!!

    NASA Astrophysics Data System (ADS)

    Gurr, Henry

    2014-03-01

    Princeton Physicist J. J. Hopfield's Mathematical Model of the Mammalian Brain, (Similar To Ising Glass Model of a crystal of magnetic spin particles) says our Brain-Work for Memory, Perception, Language, Thinking, etc, (Even the AHA-EUREKA-Flash Of Insight Type Problem Solving), is achieved by our massively inter-connected CNS Neurons ... working together ... MINIMIZING an analog of physical energy ... thus yielding Optimal Solutions: These ``best'' answers, correspond to highest mental coherence, for most facets organism response, beit mental (eg: perception, memory, ideas, thinking, etc) or physical-muscular-actions (eg speaking, tool using, trail following, etc). Our brain is this way, because living creature, MUST be evolved, so they will find & use the best actions, for survival!!! Our human heritage, is to instantly compute near optimal future plans, (mental & physical-muscular), and be able to accomplish plans reliably & efficiently. If you know of book or articles in these topic areas, please email to HenryG--USCA.edu How to work well, with your own ``self'', called mind-body, will follow!! Conjectures: Who is the ``I'' that appears to make decisions? Am ``I'' the master of my domain? Is there an ``I'' or am ``I'' merely an illusion of reality.

  17. Nonlinear phonon interferometry at the Heisenberg limit

    NASA Astrophysics Data System (ADS)

    Cheung, Hil F. H.; Patil, Yogesh Sharad; Chang, Laura; Chakram, Srivatsan; Vengalattore, Mukund

    2016-05-01

    Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ 1 /√{ N}) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. Here, we realize a prominent example of such schemes, the so-called SU(1,1) interferometer, in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ 1 / N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. We describe how our work extends the optomechanical toolbox and how it presents new avenues for studies of optomechanical sensing and studies of nonequilibrium dynamics of multimode optomechanical systems. This work was supported by the DARPA QuASAR program through a grant from the ARO, the ARO MURI on non-equilibrium manybody dynamics and an NSF INSPIRE award.

  18. Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation

    NASA Astrophysics Data System (ADS)

    Baek, So-Young; Kaneda, Fumihiro; Ozawa, Masanao; Edamatsu, Keiichi

    2013-07-01

    The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

  19. Aspects of universally valid Heisenberg uncertainty relation

    NASA Astrophysics Data System (ADS)

    Fujikawa, Kazuo; Umetsu, Koichiro

    2013-01-01

    A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs-Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs-Kelly uncertainty relation and the Heisenberg error-disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.

  20. The Natural Selection of the Chemical Elements (by R. J. P. Williams and J. J. R. Fraústo da Silva)

    NASA Astrophysics Data System (ADS)

    Kauffman, George B.

    1998-12-01

    Clarendon: New York, 1996. xxvi + 646 pp. Figs., tables. 20.5 x 25.6 cm. ISBN 0-19-855843-0. $80.00. R. J. P. Williams, Royal Society Research Professor Emeritus at Wadham College, Oxford University, and J. J. R. Fraústo da Silva, Professor of Analytical Chemistry at the Instituto Superior Técnico, Universidade Técnica de Lisboa, have collaborated on two previous volumes: New Trends in Bio-inorganic Chemistry (1978) and The Biological Chemistry of the Elements (3rd printing, 1994). Their latest collaborative effort is a book whose ambitious objective is "to show the relationship of every kind of material around us, living and nonliving, to the properties of the chemical elements of the periodic table." The "natural selection" of the chemical elements results from a number of factors, all of which are described in detail. Among these are chemical affinity related to the electronic configuration of their atoms, thermodynamic and kinetic stability, and "functional value to an organisation such as a living system". The physicist's approach to material through phase structure and the phase rule is stressed rather than the chemist's approach through bonding theories. The entire book possesses a strong environmental and interdisciplinary emphasis.

  1. Low-temperature Spin-Ice State of Quantum Heisenberg Magnets on Pyrochlore Lattice

    NASA Astrophysics Data System (ADS)

    Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris

    We establish that the isotropic spin-1/2 Heisenberg antiferromagnet on pyrochlore lattice enters a spin-ice state at low, but finite, temperature. Our conclusions are based on results of the bold diagrammatic Monte Carlo simulations that demonstrate good convergence of the skeleton series down to temperature T = J/6. The ``smoking gun'' identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for static spin-spin correlation function between the quantum Heisenberg and classical Heisenberg/Ising models at all accessible temperatures. In particular, at T/J = 1/6, the momentum dependence shows a characteristic bow-tie pattern with pinch points. By numerical analytical continuation method, we also obtain the dynamic structure factor at real frequencies, showing a diffusive spinon dynamics at pinch points and spin wave continuum along the nodal lines.?

  2. Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice

    NASA Astrophysics Data System (ADS)

    Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris

    2016-04-01

    We study the low-temperature physics of the SU(2)-symmetric spin-1 /2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T /J =1 /6 . The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T /J =1 /6 . The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.

  3. Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice.

    PubMed

    Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris

    2016-04-29

    We study the low-temperature physics of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T/J=1/6. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T/J=1/6. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.

  4. Excitations in a four-leg antiferromagnetic Heisenberg spin tube

    SciTech Connect

    Garlea, Vasile O; Zheludev, Andrey I; Regnault, L.-P.; Chung, J.-H.; Qiu, Y.; Boehm, Martin; Habicht, Klaus; Meissner, Michael

    2008-01-01

    Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu$_2$Cl$_{4}\\cdot$ D$_8$C$_4$SO$_2$. Contrary to previously conjectured models that relied on bond-alternating nearest neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a $S=1/2$ 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.

  5. Excitations in a Four-Leg Antiferromagnetic Heisenberg Spin Tube,

    SciTech Connect

    Garlea, Vasile O; Zheludev, Andrey I; Regnault, L.-P.; Chung, J.-H.; Qiu, Y.; Boehm, Martin; Habicht, Klaus; Meissner, Michael; Fernandez-Baca, Jaime A

    2008-01-01

    Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu2Cl4 D8C4SO2. Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S 1=2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.

  6. Excitations in a four-leg antiferromagnetic Heisenberg spin tube.

    PubMed

    Garlea, V O; Zheludev, A; Regnault, L-P; Chung, J-H; Qiu, Y; Boehm, M; Habicht, K; Meissner, M

    2008-01-25

    Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu(2)Cl(4).D(8)C(4)SO(2). Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S=1/2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.

  7. Heisenberg: Paralleling Scientific and Historical Methods

    NASA Astrophysics Data System (ADS)

    Cofield, Calla

    2007-04-01

    Werner Heisenberg is an important historical subject within the physics community partly because his actions as a human being are discussed nearly as often as his work as a physicist. But does the scientific community establish it's historical ideas with the same methods and standards as it's scientific conclusions? I interviewed Heisenberg's son, Jochen Heisenberg, a professor of physics at UNH. Despite a great amount of literature on Werner Heisenberg, only one historian has interviewed Jochen about his father and few have interviewed Werner's wife. Nature is mysterious and unpredictable, but it doesn't lie or distort like humans, and we believe it can give ``honest'' results. But are we keeping the same standards with history that we do with science? Are we holding historians to these standards and if not, is it up to scientists to not only be keepers of scientific understanding, but historical understanding as well? Shouldn't we record history by using the scientific method, by weighing the best sources of data differently than the less reliable, and are we right to be as stubborn about changing our views on history as we are about changing our views on nature?

  8. Naturalistic Misunderstanding of the Heisenberg Uncertainty Principle.

    ERIC Educational Resources Information Center

    McKerrow, K. Kelly; McKerrow, Joan E.

    1991-01-01

    The Heisenberg Uncertainty Principle, which concerns the effect of observation upon what is observed, is proper to the field of quantum physics, but has been mistakenly adopted and wrongly applied in the realm of naturalistic observation. Discusses the misuse of the principle in the current literature on naturalistic research. (DM)

  9. Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain.

    PubMed

    Strečka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L

    2014-02-01

    The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.

  10. Watson-Crick pairing, the Heisenberg group and Milnor invariants.

    PubMed

    Gadgil, Siddhartha

    2009-07-01

    We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

  11. Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings.

    PubMed

    Chandra, Samarth; Ramola, Kabir; Dhar, Deepak

    2010-09-01

    We analyze the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbor interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order by disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin- S Kitaev model for large S, and obtain lower and upper bounds on the ground-state energy of the quantum model.

  12. Lie symmetry analysis of the Heisenberg equation

    NASA Astrophysics Data System (ADS)

    Zhao, Zhonglong; Han, Bo

    2017-04-01

    The Lie symmetry analysis is performed on the Heisenberg equation from the statistical physics. Its Lie point symmetries and optimal system of one-dimensional subalgebras are determined. The similarity reductions and invariant solutions are obtained. Using the multipliers, some conservation laws are obtained. We prove that this equation is nonlinearly self-adjoint. The conservation laws associated with symmetries of this equation are constructed by means of Ibragimov's method.

  13. Fourier analysis on the Heisenberg group

    PubMed Central

    Geller, Daryl

    1977-01-01

    We obtain a usable characterization of the (group) Fourier transform of 𝒮(Hn) (Schwartz space on the Heisenberg group). The characterization involves writing elements of [Formula: see text] as asymptotic series in Planck's constant. In the process, we derive a new “discrete” version of spherical harmonics, and elucidate the theory of group contractions. We give an application to Hardy space theory. PMID:16578749

  14. Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings

    NASA Astrophysics Data System (ADS)

    Rojas, Onofre; Strečka, J.; de Souza, S. M.

    2016-11-01

    The spin-1/2 Ising-Heisenberg two-leg ladder accounting for alternating Ising and Heisenberg inter-leg couplings in addition to the Ising intra-leg coupling is rigorously mapped onto to a mixed spin-(3/2,1/2) Ising-Heisenberg diamond chain with the nodal Ising spins S = 3 / 2 and the interstitial spin-1/2 Heisenberg dimers. The latter effective model with higher-order interactions between the nodal and interstitial spins is subsequently exactly solved within the transfer-matrix method. The model under investigation exhibits five different ground states: ferromagnetic, antiferromagnetic, superantiferromagnetic and two types of frustrated ground states with a non-zero residual entropy. A detailed study of thermodynamic properties reveals an anomalous specific-heat peak at low enough temperatures, which is strongly reminiscent because of its extraordinary height and sharpness to an anomaly accompanying a phase transition. It is convincingly evidenced, however, that the anomalous peak in the specific heat is finite and it comes from vigorous thermal excitations from a two-fold degenerate ground state towards a macroscopically degenerate excited state. Thermal entanglement between the nearest-neighbor Heisenberg spins is also comprehensively explored by taking advantage of the concurrence. The threshold temperature delimiting a boundary between the entangled and disentangled parameter space may show presence of a peculiar temperature reentrance.

  15. Magnetic pyroxenes LiCrGe2O6 and LiCrSi2O6: Dimensionality crossover in a nonfrustrated S =3/2 Heisenberg model

    NASA Astrophysics Data System (ADS)

    Janson, O.; Nénert, G.; Isobe, M.; Skourski, Y.; Ueda, Y.; Rosner, H.; Tsirlin, A. A.

    2014-12-01

    The magnetism of magnetoelectric S =3/2 pyroxenes LiCrSi2O6 and LiCrGe2O6 is studied by density functional theory calculations, quantum Monte Carlo (QMC) simulations, neutron diffraction, as well as low- and high-field magnetization measurements. In contrast with earlier papers, we find that the two compounds feature remarkably different, albeit nonfrustrated magnetic models. In LiCrSi2O6 , two relevant exchange integrals, J1 ≃9 K along the structural chains and Jic1 ≃2 K between the chains, form a two-dimensional anisotropic honeycomb lattice. In contrast, the spin model of LiCrGe2O6 is constituted of three different exchange couplings. Surprisingly, the leading exchange Jic1 ≃2.3 K operates between the chains, while J1 ≃1.2 K is about two times smaller. The additional interlayer coupling Jic2 ≃ J1 renders this model three dimensional. QMC simulations reveal excellent agreement between our magnetic models and the available experimental data. Underlying mechanisms of the exchange couplings, magnetostructural correlations, as well as implications for other pyroxene systems are discussed.

  16. Topological Basis Method for Four-Qubit Spin-1/2 XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng

    2017-03-01

    In this paper, we investigate the four-qubit spin-1/2 XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction by topological basis method, and research the relationship between the topological basis states and the ground states. In order to study the Hamiltonian system beyond XXZ model, we introduce two Temperley-Lieb algebra generators and two other generalized generators. Then we investigate the relationship between topological basis and Heisenberg XXZ model with Dzyaloshinskii-Moriya interaction. The results show that the ground state of this model falls on the topological basis state for anti-ferromagnetic case and gapless phase case.

  17. Local Spin Relaxation within the Random Heisenberg Chain

    NASA Astrophysics Data System (ADS)

    Herbrych, J.; Kokalj, J.; Prelovšek, P.

    2013-10-01

    Finite-temperature local dynamical spin correlations Snn(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu2(Si0.5Ge0.5)2O7, which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.

  18. Spin supersolid in an anisotropic spin-one Heisenberg chain.

    PubMed

    Sengupta, P; Batista, C D

    2007-11-23

    We consider an S=1 Heisenberg chain with strong exchange (Delta=J(z)/J(perpendicular)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram using a quantum Monte Carlo method.

  19. Science 101: What, Exactly, Is the Heisenberg Uncertainty Principle?

    ERIC Educational Resources Information Center

    Robertson, Bill

    2016-01-01

    Bill Robertson is the author of the NSTA Press book series, "Stop Faking It! Finally Understanding Science So You Can Teach It." In this month's issue, Robertson describes and explains the Heisenberg Uncertainty Principle. The Heisenberg Uncertainty Principle was discussed on "The Big Bang Theory," the lead character in…

  20. Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions.

    PubMed

    Viet, Dao Xuan; Kawamura, Hikaru

    2010-08-27

    We study the issue of the spin-chirality decoupling or coupling in the ordering of the Heisenberg spin glass by performing large-scale Monte Carlo simulations on a one-dimensional Heisenberg spin-glass model with a long-range power-law interaction up to large system sizes. We find that the spin-chirality decoupling occurs for an intermediate range of the power-law exponent. Implications to the corresponding d-dimensional short-range model are discussed.

  1. Phase transition in Ising, XY and Heisenberg magnetic films

    NASA Astrophysics Data System (ADS)

    Masrour, R.; Hamedoun, M.; Benyoussef, A.

    2012-01-01

    The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τc is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces Jb, Js and J⊥, respectively. It is found that τc increases with the exchange interactions of surface. The magnetic phase diagrams (τc versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures Tc(l) from the bulk value (Tc(∞)/Tc(l) - 1) can be described by a power law l-λ, where λ = 1/υ is the inverse of the correlation length exponent.

  2. Green's function approach of an anisotropic Heisenberg ferrimagnetic system

    NASA Astrophysics Data System (ADS)

    Mert, Gülistan

    2013-12-01

    We have investigated the influence of the exchange anisotropy parameter on the magnetization, critical and compensation temperatures and susceptibility of the anisotropic Heisenberg ferrimagnetic system with the single-ion anisotropy under an external magnetic field using the double-time temperature-dependent Green's function theory. In order to decouple the higher order Green's functions, Anderson-Callen's decoupling and random phase approximations have been used. This model is useful for understanding the temperature dependence of total magnetization of Lithium-chromium ferrites Li0.5Fe1.25Cr1.25O4 for which negative magnetization is characteristic. We observe that the critical temperature increases when the exchange anisotropy increases. When the system is under an external magnetic field, one obtains the first-order phase transition where the magnetization jumps for all the values of the exchange anisotropy parameters.

  3. The elusive Heisenberg limit in quantum-enhanced metrology

    PubMed Central

    Demkowicz-Dobrzański, Rafał; Kołodyński, Jan; Guţă, Mădălin

    2012-01-01

    Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. PMID:22990859

  4. Tsallis Entropy Composition and the Heisenberg Group

    NASA Astrophysics Data System (ADS)

    Kalogeropoulos, Nikos

    2013-03-01

    We present an embedding of the Tsallis entropy into the three-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition induces fractal properties on the underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we justify why the underlying configuration/phase space of systems described by the Tsallis entropy has polynomial growth for both discrete and Riemannian cases. We provide a geometric framework that elucidates Abe's formula for the Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian spaces.

  5. Generalized Weyl-Heisenberg (GWH) groups

    NASA Astrophysics Data System (ADS)

    Ghaani Farashahi, Arash

    2014-09-01

    Let be a locally compact group, be a locally compact Abelian (LCA) group, be a continuous homomorphism, and let be the semi-direct product of and with respect to the continuous homomorphism . In this article, we introduce the Generalized Weyl-Heisenberg (GWH) group associate with the semi-direct product group . We will study basic properties of from harmonic analysis aspects. Finally, we will illustrate applications of these methods in the case of some well-known semi-direct product groups.

  6. Quantum Disordered State without Frustration in the Double Layer Heisenberg Antiferromagnet —Dimer Expansion and Projector Monte Carlo Study—

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    1992-03-01

    The quantum disordered state (QDOS) of the spin 1/2 double layer square lattice Heisenberg antiferromagnet is studied. Using the dimer expansion from the limit of the large interlayer coupling J', the staggered susceptibility χ, the antiferromagnetic structure factor Sπ and the antiferromagnetic correlation length ξ are calculated up to the 6-th order in the intralayer coupling J. The ratio analysis shows that the QDOS becomes unstable against the Néel ordering at J'/J≃2.56. The critical exponents are not inconsistent with the universality class of the 3-dimensional classical Heisenberg model, suggesting that our QDOS corresponds to that expected in the 2-dimensional square lattice Heisenberg antiferromagnet with unphysically small spin (<0.276). The results of the projector Monte Carlo simulation also confirms the dimer expansion results.

  7. Heisenberg and the Framework of Science Policy

    NASA Astrophysics Data System (ADS)

    Carson, Cathryn

    2003-09-01

    In the decades after 1945, new structures were created for science policy in the Federal Republic. To the establishment of the post war framework Heisenberg contributed as much as any other figure. This was true even though, on the whole, he took no great pleasure in the venture, nor was he always particularly adept at it. His conceptions revolved around certain key notions: autonomy and centralization, elite advisory bodies and relationships of trust, modernization and international standards. These show up at many levels of his activity, from the Max Planck Society to national and international advisory committees to the Humboldt Foundation itself. His opinions were shaped by encounters in the Federal Republic, but they also grew out of his experience of the Third Reich. At a moment like the present, when the post war settlement is under review, it is interesting to reflect on the inherited system: on the extent to which it reflects the situation of the post war decades and the intuitions of those who, like Heisenberg, created it.

  8. Teleportation via thermally entangled states of a two-qubit Heisenberg XX chain

    SciTech Connect

    Yeo Ye

    2002-12-01

    Recently, entanglement teleportation has been investigated by Lee and Kim [Phys. Rev. Lett. 84, 4236 (2000)]. In this paper we study entanglement teleportation via two separate thermally entangled states of a two-qubit Heisenberg XX chain. We established the condition under which the parameters of the model have to satisfy in order to teleport entanglement. The necessary minimum amount of thermal entanglement for some fixed strength of exchange coupling is a function of the magnetic field and the temperature.

  9. Susceptibility of the 2D spin-1 / 2 Heisenberg antiferromagnet with an impurity.

    PubMed

    Höglund, Kaj H; Sandvik, Anders W

    2003-08-15

    We use a quantum Monte Carlo method (stochastic series expansion) to study the effects of a magnetic or nonmagnetic impurity on the magnetic susceptibility of the two-dimensional Heisenberg antiferromagnet. At low temperatures, we find a log-divergent contribution to the transverse susceptibility. We also introduce an effective few-spin model that can quantitatively capture the differences between magnetic and nonmagnetic impurities at high and intermediate temperatures.

  10. N-leg spin-S Heisenberg ladders: A density-matrix renormalization group study

    NASA Astrophysics Data System (ADS)

    Ramos, F. B.; Xavier, J. C.

    2014-03-01

    We investigate the N-leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap Δs and of the ground-state energy per site e∞N in the thermodynamic limit for ladders with widths up to six legs and spin S≤5/2. We also estimate the ground-state energy per site e∞2D for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.

  11. Heisenberg Uncertainty and the Allowable Masses of the Up Quark and Down Quark

    NASA Astrophysics Data System (ADS)

    Orr, Brian

    2004-05-01

    A possible explanation for the inability to attain deterministic measurements of an elementary particle's energy, as given by the Heisenberg Uncertainty Principle, manifests itself in an interesting anthropic consequent of Andrei Linde's Self-reproducing Inflationary Multiverse model. In Linde's model, the physical laws and constants that govern our universe adopt other values in other universes, due to variable Higgs fields. While the physics in our universe allow for the advent of life and consciousness, the physics necessary for life are not likely to exist in other universes -- Linde demonstrates this through a kind of Darwinism for universes. Our universe, then, is unique. But what are the physical laws and constants that make our universe what it is? Craig Hogan identifies five physical constants that are not bound by symmetry. Fine-tuning these constants gives rise to the basic behavior and structures of the universe. Three of the non-symmetric constants are fermion masses: the up quark mass, the down quark mass, and the electron mass. I will explore Linde's and Hogan's works by comparing the amount of uncertainty in quark masses, as calculated from the Heisenberg Uncertainty Principle, to the range of quark mass values consistent with our observed universe. Should the fine-tuning of the up quark and down quark masses be greater than the range of Heisenberg uncertainties in their respective masses (as I predict, due to quantum tunneling), then perhaps there is a correlation between the measured Heisenberg uncertainty in quark masses and the fine-tuning of masses required for our universe to be as it is. Hogan; "Why the Universe is Just So;" Reviews of Modern Physics; Issue 4; Vol. 72; pg. 1149-1161; Oct. 2000 Linde, "The Self-Reproducing Inflationary Universe;" Scientific American; No. 5; Vol. 271; pg. 48-55; Nov. 1994

  12. Heisenberg's Uncertainty Principle and Interpretive Research in Science Education.

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael

    1993-01-01

    Heisenberg's uncertainty principle and the derivative notions of interdeterminacy, uncertainty, precision, and observer-observed interaction are discussed and their applications to social science research examined. Implications are drawn for research in science education. (PR)

  13. Whittaker modules for the twisted Heisenberg-Virasoro algebra

    SciTech Connect

    Liu Dong; Wu Yuezhu; Zhu Linsheng

    2010-02-15

    We define Whittaker modules for the twisted Heisenberg-Virasoro algebra and obtain several results from the classical setting, including a classification of simple Whittaker modules by central characters.

  14. Quasi-Linear Algebras and Integrability (the Heisenberg Picture)

    NASA Astrophysics Data System (ADS)

    Vinet, Luc; Zhedanov, Alexei

    2008-02-01

    We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems.

  15. Callen-like method for the classical Heisenberg ferromagnet

    NASA Astrophysics Data System (ADS)

    Campana, L. S.; Cavallo, A.; De Cesare, L.; Esposito, U.; Naddeo, A.

    2012-02-01

    A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function's framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest.

  16. NMR spin relaxation rates in the Heisenberg bilayer

    NASA Astrophysics Data System (ADS)

    Mendes, Tiago; Curro, Nicholas; Scalettar, Richard; Paiva, Thereza; Dos Santos, Raimundo R.

    One of the striking features of heavy fermions is the fact that in the vicinity of a quantum phase transition these systems exhibit the breakdown of Fermi-liquid behavior and superconductivity. Nuclear magnetic resonance (NMR) expirements play an important role in the study of these phenomena. Measurements of NMR spin relaxation rates and Knight shift, for instance, can be used to probe the electronic spin susceptibility of these systems. Here we studied the NMR response of the Heisenberg bilayer model. In this model, it is well known that the increase of the interplane coupling between the planes, Jperp, supresses the antiferromagnetic order at a quantum critical point (QCP). We use stochastic series expansion (SSE) and the maximum-entropy analytic continuation method to calculate the NMR spin lattice relaxation rate 1 /T1 and the spin echo decay 1 /T2 G as function of Jperp. The spin echo decay, T2 G increases for small Jperp, due to the increase of the order parameter, and then vanishes abruptly in the QCP. The effects of Jperp dilution disorder in the QCP and the relaxation rates are also discussed. This research was supported by the NNSA Grant Number DE-NA 0002908, and Ciência sem fronteiras program/CNPQ.

  17. Variational Monte Carlo investigation of SU (N ) Heisenberg chains

    NASA Astrophysics Data System (ADS)

    Dufour, Jérôme; Nataf, Pierre; Mila, Frédéric

    2015-05-01

    Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU (N) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with m models have been studied for arbitrary N and m with non-Abelian bosonization [I. Affleck, Nucl. Phys. B 265, 409 (1986), 10.1016/0550-3213(86)90167-7; I. Affleck, Nucl. Phys. B 305, 582 (1988), 10.1016/0550-3213(88)90117-4], leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. Using exact diagonalization and variational Monte Carlo based on Gutzwiller projected fermionic wave functions, we have been able to verify these predictions for a representative number of cases with N ≤10 and m ≤N /2 , and we have shown that the opening of a gap is associated to a spontaneous dimerization or trimerization depending on the value of m and N . We have also investigated the marginal cases where Abelian bosonization did not lead to any prediction. In these cases, variational Monte Carlo predicts that the ground state is critical with exponents consistent with conformal field theory.

  18. Linear dependencies in Weyl-Heisenberg orbits

    NASA Astrophysics Data System (ADS)

    Dang, Hoan Bui; Blanchfield, Kate; Bengtsson, Ingemar; Appleby, D. M.

    2013-11-01

    Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which arises from the torsion points of a certain elliptic curve). This connection with elliptic curves is signalled by the presence of linear dependencies among the SIC vectors. Here we look for analogous connections between SICs and algebraic geometry by performing computer searches for linear dependencies in higher dimensional SICs. We prove that linear dependencies will always emerge in Weyl-Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix. This includes SICs when the dimension is divisible by 3 or equal to 8 mod 9. We examine the linear dependencies in dimension 6 in detail and show that smaller dimensional SICs are contained within this structure, potentially impacting the SIC existence problem. We extend our results to look for linear dependencies in orbits when the fiducial vector lies in an eigenspace of other elements of the Clifford group that are not order 3. Finally, we align our work with recent studies on representations of the Clifford group.

  19. Determination of the W W polarization fractions in p p →W±W±j j using a deep machine learning technique

    NASA Astrophysics Data System (ADS)

    Searcy, Jacob; Huang, Lillian; Pleier, Marc-André; Zhu, Junjie

    2016-05-01

    The unitarization of the longitudinal vector boson scattering (VBS) cross section by the Higgs boson is a fundamental prediction of the Standard Model which has not been experimentally verified. One of the most promising ways to measure VBS uses events containing two leptonically decaying same-electric-charge W bosons produced in association with two jets. However, the angular distributions of the leptons in the W boson rest frame, which are commonly used to fit polarization fractions, are not readily available in this process due to the presence of two neutrinos in the final state. In this paper we present a method to alleviate this problem by using a deep machine learning technique to recover these angular distributions from measurable event kinematics and demonstrate how the longitudinal-longitudinal scattering fraction could be studied. We show that this method doubles the expected sensitivity when compared to previous proposals.

  20. Quantum critical behavior of low-dimensional spin 1/2 Heisenberg antiferromagnets

    NASA Astrophysics Data System (ADS)

    Stone, Matthew Brandon

    In this dissertation, experiments on four different insulating antiferromagnetic spin 1/2 Heisenberg systems are presented and described. Copper pyrazine dinitrate is a linear chain spin 1/2 (S = 1/2) Heisenberg antiferromagnet. In an applied magnetic field, the continuum splits into multiple continua including incommensurate gapless excitations. The inelastic neutron scattering measurements presented represent the first complete experimental study of the S = 1/2 linear chain excitation spectrum in an applied magnetic field. Copper nitrate is a S = 1/2 alternating chain Heisenberg antiferromagnet. This system is near the isolated dimer limit, such that perturbation theory based on weakly coupled spin pairs accurately describes the excitation spectrum. Inelastic neutron scattering measurements were performed as a function of applied magnetic field. The data presented here represent the first such measure in all portions of the magnetic phase diagram of a gapped quantum magnet. Piperazinium hexachlorodicuprate is a two-dimensional S = 1/2 Heisenberg antiferromagnet. It is shown in this work that the structure consists of a collection of coupled spins in the crystalline ac plane. Multiple spin-spin interactions are important in this material. This has consequences for the nature of the dominant interactions and causes there to be significant spin frustration in this system. The spectrum consists of coherent dispersive singlet-triplet excitations describable in terms of multiple significant exchange interactions with geometrical frustration. Thermodynamic and inelastic neutron scattering measurements are presented which characterize the magnetic excitations as a function of temperature and applied magnetic field. In addition, the full magnetic phase diagram including a gapless disordered phase and a reentrant phase transition is presented. Cu2(1,4-diazacycloheptane)2Cl4 was widely believed to be a S = 1/2 Heisenberg spin-ladder material. Neutron scattering measurements

  1. Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

    PubMed

    Kvashnin, Y O; Cardias, R; Szilva, A; Di Marco, I; Katsnelson, M I; Lichtenstein, A I; Nordström, L; Klautau, A B; Eriksson, O

    2016-05-27

    By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

  2. Field dependent spin transport of anisotropic Heisenberg chain

    NASA Astrophysics Data System (ADS)

    Rezania, H.

    2016-04-01

    We have addressed the static spin conductivity and spin Drude weight of one-dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg chain in the finite magnetic field. We have investigated the behavior of transport properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on the spin transport properties has also been studied via the bosonic model by Green's function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the spin conductivity and spin Drude weight in the gapped field induced spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of static spin conductivity and Drude weight for various anisotropy parameters. Our results show the regular part of spin conductivity vanishes in isotropic case however Drude weight has a finite non-zero value and the system exhibits ballistic transport properties. We also find the peak in the static spin conductivity factor moves to higher temperature upon increasing the magnetic field at fixed anisotropy. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of spin Drude weight for different magnetic field and various anisotropy parameters.

  3. Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet

    NASA Astrophysics Data System (ADS)

    Ma, Nv-Sen; Sandvik, Anders W.; Yao, Dao-Xin

    2015-09-01

    We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J1 and interlayer interaction J2. Below the classical percolation threshold pc, the system has three phases reachable by tuning the interaction ratio g = J2/J1: a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χu exp(-b/Tα) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O(3) universality class in 2+1 dimensions.

  4. Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets

    NASA Astrophysics Data System (ADS)

    Schwandt, David; Alet, Fabien; Oshikawa, Masaki

    2014-03-01

    Every singlet state of a quantum spin-1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the singlet state and are key ingredients in variational calculations. In this work, we study the bipartite valence bond distributions and their correlations within the ground state of the Heisenberg antiferromagnet on bipartite lattices. In terms of field theory, this problem can be mapped to correlation functions near a boundary. In dimension d ≥2, a nonlinear σ model analysis reveals that at long distances the probability distribution P (r) of valence bond lengths decays as |r|-d-1 and that valence bonds are uncorrelated. By a bosonization analysis, we also obtain P(r )∝|r|-d-1 in d =1 despite the different mechanism. On the other hand, we find that correlations between valence bonds are important even at large distances in d =1, in stark contrast to d ≥2. The analytical results are confirmed by high-precision quantum Monte Carlo simulations in d =1, 2, and 3. We develop a single-projection loop variant of the valence bond projection algorithm, which is well designed to compute valence bond probabilities and for which we provide algorithmic details.

  5. A quaternionic map for the steady states of the Heisenberg spin-chain

    NASA Astrophysics Data System (ADS)

    Mehta, Mitaxi P.; Dutta, Souvik; Tiwari, Shubhanshu

    2014-01-01

    We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.

  6. Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction.

    PubMed

    Chen, Shu; Wang, Li; Gu, Shi-Jian; Wang, Yupeng

    2007-12-01

    In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J1-J2 model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J1-J2 model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.

  7. Spin-1/2 Heisenberg Antiferromagnet on the Spatially Anisotropic Kagome Lattice

    NASA Astrophysics Data System (ADS)

    Schnyder, Andreas; Starykh, Oleg; Balents, Leon

    2008-03-01

    We study the quasi-one-dimensional limit of the Spin-1/2 quantum antiferromagnet on the Kagome lattice, a model Hamiltonian that might be of relevance for the mineral volborthite [1,2]. The lattice is divided into antiferromagnetic spin-chains (exchange J) that are weakly coupled via intermediate ``dangling'' spins (exchange J'). Using bosonization, renormalization group methods, and current algebra techniques we determine the ground state as a function of J'/J. The case of a strictly one-dimensional Kagome strip is also discussed. [1] Z. Hiroi, M. Hanawa, N. Kobayashi, M. Nohara, Hidenori Takagi, Y. Kato, and M. Takigawa, J. Phys. Soc. Japan 70, 3377 (2001). [2] F. Bert, D. Bono, P. Mendels, F. Ladieu, F. Duc, J.-C. Trumbe, and P. Millet, Phys. Rev. Lett. 95, 087203 (2005).

  8. Quantum signatures of breathers in a finite Heisenberg spin chain.

    PubMed

    Djoufack, Z I; Kenfack-Jiotsa, A; Nguenang, J P; Domngang, S

    2010-05-26

    A map of a quantum Heisenberg spin chain into an extended Bose-Hubbard-like Hamiltonian is set up. Within this framework, the spectrum of the corresponding Bose-Hubbard chain, on a periodic one-dimensional lattice containing two, four, and six bosons shows interesting detailed band structures. These fine structures are studied using numerical diagonalization, and nondegenerate and degenerate perturbation theory. We also focus our attention on the effect of the anisotropy and Heisenberg exchange energy on the detailed band structures. The signature of the quantum breather is also set up by the square of the amplitudes of the corresponding eigenvectors in real space.

  9. Geometrically frustrated Cairo pentagonal lattice stripe with Ising and Heisenberg exchange interactions

    NASA Astrophysics Data System (ADS)

    Rodrigues, F. C.; de Souza, S. M.; Rojas, Onofre

    2017-04-01

    Motivated by the recent discoveries of some compounds such as the Bi2Fe4O9 which crystallizes in an orthorhombic crystal structure with the Fe3+ ions, and iron-based oxyfluoride Bi4Fe5O13 F compounds following the pattern of Cairo pentagonal structure, among some other compounds. We propose a model for one stripe of the Cairo pentagonal Ising-Heisenberg lattice, one of the edges of a pentagon is different, and this edge will be associated with a Heisenberg exchange interaction, while the Ising exchange interactions will associate the other edges. We study the phase transition at zero temperature, illustrating five phases: a ferromagnetic phase (FM), a dimer antiferromagnetic (DAF), a plaquette antiferromagnetic (PAF), a typical antiferromagnetic (AFM) and a peculiar frustrated phase (FRU) where two types of frustrated states with the same energy coexist. To obtain the partition function of this model, we use the transfer matrix approach and following the eight vertex model notation. Using this result we discuss the specific heat, internal energy and entropy as a function of the temperature, and we can observe some unexpected behavior in the low-temperature limit, such as anomalous double peak in specific heat due to the existence of three phase (FRU, PAF(AFM) and FM) transitions occurring in a close region to each other. Consequently, the low-lying energy thermal excitation generates this double anomalous peak, and we also discuss the internal energy at the low temperature limit, where this double peak curve occurs. Some properties of our result were compared with two dimensional Cairo pentagonal lattices, as well as orthogonal dimer plaquette Ising-Heisenberg chain.

  10. New Universality Class in Spin-One-Half Fibonacci Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2004-07-01

    Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.

  11. Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice.

    PubMed

    Aoyama, Kazushi; Kawamura, Hikaru

    2016-06-24

    Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2,1/2,1/2) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed.

  12. Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice

    NASA Astrophysics Data System (ADS)

    Aoyama, Kazushi; Kawamura, Hikaru

    2016-06-01

    Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2 ,1/2 ,1/2 ) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed.

  13. New universality class in spin-one-half Fibonacci Heisenberg chains.

    PubMed

    Hida, Kazuo

    2004-07-16

    Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.

  14. Double-well atom trap for fluorescence detection at the Heisenberg limit

    NASA Astrophysics Data System (ADS)

    Stroescu, Ion; Hume, David B.; Oberthaler, Markus K.

    2015-01-01

    We experimentally demonstrate an atom number detector capable of simultaneous detection of two mesoscopic ensembles with single-atom resolution. Such a sensitivity is a prerequisite for quantum metrology at a precision approaching the Heisenberg limit. Our system is based on fluorescence detection of atoms in a hybrid trap in which a dipole barrier divides a magneto-optical trap into two separated wells. We introduce a noise model describing the various sources contributing to the measurement error and report a limit of up to 500 atoms for single-atom resolution in the atom number difference.

  15. Strong anisotropy within a Heisenberg model in the Jeff=12 insulating state of Sr2Ir0.8Ru0.2O4

    SciTech Connect

    Calder, Stuart A.; Kim, J. W.; Taylor, Alice E.; Upton, M. H.; Casa, D.; Cao, Guixin; Mandrus, D.; Lumsden, Mark D.; Christianson, Andrew D.

    2016-12-28

    The dispersive magnetic excitations in Sr2IrO4 have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La2CuO4. In this paper, we investigate the inelastic spectra of Sr2Ir0.8Ru0.2O4 with resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr2IrO4; however, the disorder induced by the substitution of 20% Ir4+ ions for Ru4+ removes longer range exchange interactions. A large spin gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due to the altered magnetic structure in Sr2Ir0.8Ru0.2O4 with c-axis aligned moments compared to the basal plane moments in the parent. Finally, collectively the results indicate the robustness of a Heisenberg model description even when the magnetic structure is altered and the Jeff = 1/2 moments are diluted.

  16. Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Wan, Yuan; Gingras, Michel J. P.

    2016-11-01

    We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground-state manifold of the model contains an extensively large family of noncoplanar spin states known as "color ice states." Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membranelike" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and elucidate their physical properties. Furthermore, we study the order by disorder phenomenon in this model, focusing on the role of harmonic fluctuations. Our computationally limited phase space search suggests that quantum fluctuations select three different states as the magnitude of the biquadratic interaction increases relative to the bilinear interaction, implying a sequence of phase transitions solely driven by fluctuations.

  17. Heisenberg uncertainty principles for an oscillatory integral operator

    NASA Astrophysics Data System (ADS)

    Castro, L. P.; Guerra, R. C.; Tuan, N. M.

    2017-01-01

    The main aim of this work is to obtain Heisenberg uncertainty principles for a specific oscillatory integral operator which representatively exhibits different parameters on their sine and cosine phase components. Additionally, invertibility theorems, Parseval type identities and Plancherel type theorems are also obtained.

  18. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    NASA Astrophysics Data System (ADS)

    Nocera, A.; Patel, N. D.; Fernandez-Baca, J.; Dagotto, E.; Alvarez, G.

    2016-11-01

    We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small as U /t ˜2 -3 , although ratios of peak intensities at different momenta continue evolving with increasing U /t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U /t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

  19. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    DOE PAGES

    Nocera, Alberto; Patel, Niravkumar D.; Fernandez-Baca, Jaime A.; ...

    2016-11-28

    In this paper, we study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small asmore » U/t ~ 2–3, although ratios of peak intensities at different momenta continue evolving with increasing U/t converging only slowly to the Heisenberg limit. Finally, we discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.« less

  20. Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

    SciTech Connect

    Nocera, Alberto; Patel, Niravkumar D.; Fernandez-Baca, Jaime A.; Dagotto, Elbio R.; Alvarez, Gonzalo

    2016-11-28

    In this paper, we study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small as U/t ~ 2–3, although ratios of peak intensities at different momenta continue evolving with increasing U/t converging only slowly to the Heisenberg limit. Finally, we discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

  1. Excitation spectra of generalized antiferromagnetic Heisenberg spin chains (abstract)

    NASA Astrophysics Data System (ADS)

    Parkinson, J. B.; Bonner, J. C.

    1988-04-01

    We compare the excitation spectra in the presence of a magnetic field of a number of integrable (exactly solvable) and nonintegrable quantum spin chains of various spin value s. The archetypal Bethe-ansatz integrable model is the s= 1/2 Heisenberg antiferromagnet (HB AFM). The excitation spectra are characterized by a soft mode which tracks across the Brillouin zone as the field increases to its saturation value. A class of Bethe-ansatz integrable models with SU(2) symmetry and the general spin s display excitation spectra qualitatively similar to the spin- 1/2 model above, for all s. A second class of Bethe-ansatz integrable models has SU(n) symmetry, where n=2s+1. Like the SU(2) integrable chains, these models have gapless excitation spectra, but the basic Brillouin zone changes from k=±2π/(2s+1)a. Studies show that periodicity of the SU(3) member of the class changes (increases) as the field increases to saturation. For both classes of integrable models, there is a single type of excitation pattern which is generically similar for all s. In the case of the other models, on the other hand, numerical studies show that the excitations divide into at least two distinct classes. In the case of the s=1 HB AFM, at high fields (corresponding to SzT=N,N-1, . . .,N/2) the excitations map approximately onto the complete set of excitations for s= 1/2 , whereas at low fields (SzT=N/2,N/2-1,. . .,0) the excitations have notable classical character. In the case of the s=1 model with pure biquadratic exchange, one set of excitations, corresponding to SzT even (SzT=N,N-2,. . .,2,0), again shows an approximate mapping to the complete excitation set for s= 1/2 . The second class of excitations, corresponding to SzT odd, are very different. They are symmetric about k=±π/2a for all SzT, i.e., correspond to a basic Brillouin zone of ±π/2a.

  2. Spin structure factors of Heisenberg spin chain in the presence of anisotropy and magnetic field

    NASA Astrophysics Data System (ADS)

    Rezania, H.

    2017-02-01

    We have theoretically studied the spin structure factors of spin chain in the presence of longitudinal field and transverse anisotropy. The possible effects of easy axis magnetization are investigated in terms of anisotropy in the Heisenberg interactions. This anisotropy is considered for exchange coupling constants perpendicular to magnetic field direction. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the longitudinal structure factor at fixed value for anisotropy moves to higher frequency with magnetic field. Also the intensity of dynamical structure factor decreases with magnetic field. A small dependence of longitudinal dynamical spin structure factor on the anisotropy is observed for fixed value of magnetic field. Our results show longitudinal static structure factor is found to be monotonically increasing with magnetic field due to increase of spins aligning along magnetic field. Furthermore the dispersion behaviors of static longitudinal and transverse structure factors for different magnetic fields and anisotropy parameters are addressed.

  3. Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

    SciTech Connect

    Zhang, Guo-Feng

    2007-03-15

    Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic.

  4. Properties of the random-singlet phase: From the disordered Heisenberg chain to an amorphous valence-bond solid

    NASA Astrophysics Data System (ADS)

    Shu, Yu-Rong; Yao, Dao-Xin; Ke, Chih-Wei; Lin, Yu-Cheng; Sandvik, Anders W.

    2016-11-01

    We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S =1 /2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multispin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (singlet pair) basis from a contribution that cannot be generated by the SDRG scheme. In the model with multispin couplings, where the clean system dimerizes spontaneously, random singlets form between spinons localized at domain walls in the presence of disorder. This amorphous valence-bond solid is asymptotically a random-singlet state and only differs from the random-exchange Heisenberg chain in its short-distance properties.

  5. Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction

    NASA Astrophysics Data System (ADS)

    Surungan, Tasrief; Bansawang B., J.; Tahir, Dahlang

    2016-03-01

    Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.

  6. Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo; Affleck, Ian

    2005-06-01

    The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chain is known to exhibit a 3-fold degenerate \\uparrow\\downarrow\\uparrow-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the \\bullet\\hskip -1pt-\\hskip -1pt\\bullet \\uparrow-type quantum plateau state (\\bullet\\hskip -1pt-\\hskip -1pt\\bullet = singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact \\bullet\\hskip -1pt-\\hskip -1pt\\bullet \\uparrow-type quantum plateau state, is also presented. The phase transition to the classical \\uparrow\\downarrow\\uparrow-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.

  7. Functional renormalization group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice

    NASA Astrophysics Data System (ADS)

    Hering, Max; Reuther, Johannes

    2017-02-01

    We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated J1-J2 kagome-Heisenberg model using the pseudofermion functional renormalization group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of noncollinear magnetic orders of the J1-J2 Heisenberg model (q =0 , √{3 }×√{3 } , and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral herbertsmithite which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicate that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for herbertsmithite, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.

  8. Search for the Heisenberg spin glass on rewired cubic lattices with antiferromagnetic interaction

    NASA Astrophysics Data System (ADS)

    Surungan, Tasrief

    2016-10-01

    Spin glass (SG) is a typical magnetic system which is mainly characterized by a frozen random spin orientation at low temperatures. Frustration and randomness are considered to be the key ingredients for the existence of SGs. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] found that the antiferromagnetic (AF) Ising spins on scale free network (SFN) exhibited SG behavior. This is purely AF system, a new type of SG different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely due to a topological factor and its randomness is brought by irregular connectivity. Recently, it was reported that the AF Heisenberg model on SFN exhibited SG behavior [Surungan et al., JPCS, 640, 012005 (2015)/doi:10.1088/1742-6596/640/1/012005]. In order to accommodate the notion of spatial dimension, we further investigated this type of system by studying an AF Heisenberg model on rewired cubic lattices, constructed by adding one extra bond randomly connecting each spin to one of its next-nearest neighbors. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.

  9. Quantized antiferromagnetic spin waves in the molecular Heisenberg ring CsFe8

    NASA Astrophysics Data System (ADS)

    Dreiser, J.; Waldmann, O.; Dobe, C.; Carver, G.; Ochsenbein, S. T.; Sieber, A.; Güdel, H. U.; van Duijn, J.; Taylor, J.; Podlesnyak, A.

    2010-01-01

    We report on inelastic neutron-scattering (INS) measurements on the molecular spin ring CsFe8 , in which eight spin-5/2 Fe(III) ions are coupled by nearest-neighbor antiferromagnetic Heisenberg interaction. We have recorded INS data on a nondeuterated powder sample up to high energies at the time-of-flight spectrometers FOCUS at PSI and MARI at ISIS, which clearly show the excitation of spin waves in the ring. Due to the small number of spin sites, the spin-wave dispersion relation is not continuous but quantized. Furthermore, the system exhibits a gap between the ground state and the first excited state. We have modeled our data using exact diagonalization of a Heisenberg-exchange Hamiltonian together with a small single-ion anisotropy term. Due to the molecule’s symmetry, only two parameters J and D are needed to obtain excellent agreement with the data. The results can be well described within the framework of the rotational-band model as well as antiferromagnetic spin-wave theories.

  10. Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions

    NASA Astrophysics Data System (ADS)

    Mei, Zhongtao; Bolech, C. J.

    2017-03-01

    Using the algebraic Bethe Ansatz, we derive a matrix product representation of the exact Bethe-Ansatz states of the six-vertex Heisenberg chain (either X X X or X X Z and spin-1/2 ) with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. This result is generic for any non-nested integrable model, as is clear from our derivation, and we further show this by providing an additional example of the same matrix product state construction for a well-known model of a gas of interacting bosons. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries, and thus they suggest generic ways of exploiting (emergent) translational invariance both for finite size and in the thermodynamic limit.

  11. Fundamental uncertainty limit of optical flow velocimetry according to Heisenberg's uncertainty principle.

    PubMed

    Fischer, Andreas

    2016-11-01

    Optical flow velocity measurements are important for understanding the complex behavior of flows. Although a huge variety of methods exist, they are either based on a Doppler or a time-of-flight measurement principle. Doppler velocimetry evaluates the velocity-dependent frequency shift of light scattered at a moving particle, whereas time-of-flight velocimetry evaluates the traveled distance of a scattering particle per time interval. Regarding the aim of achieving a minimal measurement uncertainty, it is unclear if one principle allows to achieve lower uncertainties or if both principles can achieve equal uncertainties. For this reason, the natural, fundamental uncertainty limit according to Heisenberg's uncertainty principle is derived for Doppler and time-of-flight measurement principles, respectively. The obtained limits of the velocity uncertainty are qualitatively identical showing, e.g., a direct proportionality for the absolute value of the velocity to the power of 32 and an indirect proportionality to the square root of the scattered light power. Hence, both measurement principles have identical potentials regarding the fundamental uncertainty limit due to the quantum mechanical behavior of photons. This fundamental limit can be attained (at least asymptotically) in reality either with Doppler or time-of-flight methods, because the respective Cramér-Rao bounds for dominating photon shot noise, which is modeled as white Poissonian noise, are identical with the conclusions from Heisenberg's uncertainty principle.

  12. Numerical investigation of the role of topological defects in the three-dimensional Heisenberg transition

    NASA Astrophysics Data System (ADS)

    Lau, Man-Hot; Dasgupta, Chandan

    1989-04-01

    The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a ``chemical potential'' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to the paramagnetic phase to occur.

  13. Investigation of non-Hermitian Hamiltonians in the Heisenberg picture

    NASA Astrophysics Data System (ADS)

    Miao, Yan-Gang; Xu, Zhen-Ming

    2016-05-01

    The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed.

  14. Quaternionic Heisenberg groups as naturally reductive homogeneous spaces

    NASA Astrophysics Data System (ADS)

    Agricola, Ilka; Ferreira, Ana Cristina; Storm, Reinier

    2015-05-01

    In this paper, we describe the geometry of the quaternionic Heisenberg groups from a Riemannian viewpoint. We show, in all dimensions, that they carry an almost 3-contact metric structure which allows us to define the metric connection that equips these groups with the structure of a naturally reductive homogeneous space. It turns out that this connection, which we shall call the canonical connection because of its analogy to the 3-Sasaki case, preserves the horizontal and vertical distributions and even the quaternionic contact (qc) structure of the quaternionic Heisenberg groups. We focus on the 7-dimensional case and prove that the canonical connection can also be obtained by means of a cocalibrated G2 structure. We then study the spinorial properties of this group and present the noteworthy fact that it is the only known example of a manifold which carries generalized Killing spinors with three different eigenvalues.

  15. Heisenberg-limited Sagnac interferometer with multiparticle states

    NASA Astrophysics Data System (ADS)

    Luo, Chengyi; Huang, Jiahao; Zhang, Xiangdong; Lee, Chaohong

    2017-02-01

    The Sagnac interferometry has widely been used to measure rotation frequency. Beyond the conventional single-particle scheme, we propose a multiparticle scheme via Bose condensed atoms. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring via a state-dependent rotating potential, and then the atoms are recombined for interference via Ramsey pulses. The phase accumulation time is determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated, and the achieved measurement precisions approach the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision rotation sensing.

  16. Path integral quantization corresponding to the deformed Heisenberg algebra

    SciTech Connect

    Pramanik, Souvik; Moussa, Mohamed; Faizal, Mir; Ali, Ahmed Farag

    2015-11-15

    In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.

  17. Rogue waves and breathers in Heisenberg spin chain

    NASA Astrophysics Data System (ADS)

    Mukhopadhyay, Aritra K.; Vyas, Vivek M.; Panigrahi, Prasanta K.

    2015-07-01

    Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.

  18. Finite Heisenberg-Weyl Groups and Golay Complementary Sequences

    DTIC Science & Technology

    2006-01-01

    insight into the nature of these sequences , as well as a mechanism for designing sequences with desirable correlation properties. Libraries of... nature of these codes, and a new technique for their analysis, as well as a mechanism for designing sequences with desirable correla- tion properties...dimensional discrete Heisenberg-Weyl group over the field Z2. Our methodology provides a different insight into the nature of these sequences , as well as a

  19. Non-Heisenberg states of the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Dechoum, K.; França, H. M.

    1995-11-01

    The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form <(δx 2) ><(δp) 2 >=(h'/2) 2, which includes the limit of zero indeterminacy (h → 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy hΩ 0 /2 and <(δx) 2 ><(δp) 2 >=h 2 /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states.

  20. [Carl Friedrich von Weizsäcker and Werner Heisenberg].

    PubMed

    Cassidy, David C

    2014-01-01

    The 50-year relationship between Weizsäcker and Heisenberg spanned the highpoints of discovery and dictatorship during the 1930s, extended into the war-time uranium project, the post-war controversy over that project, debates over West German nuclear policy, and the philosophical implications of modern physics. This paper explores the interaction between these two leading figures during that difficult and significant half-century.

  1. Modern or Anti-modern Science? Weimar Culture, Natural Science and the Heidegger-Heisenberg Exchange

    NASA Astrophysics Data System (ADS)

    Carson, Cathryn

    The following sections are included: * Weimar Culture and Scientific Rationality * Heidegger Read Historically * Science and Crisis * Quantum Mechanics and the Heidegger-Heisenberg Exchange * Conclusion * Acknowledgments

  2. Generalized coherent states for polynomial Weyl-Heisenberg algebras

    NASA Astrophysics Data System (ADS)

    Kibler, Maurice R.; Daoud, Mohammed

    2012-08-01

    It is the aim of this paper to show how to construct á la Perelomov and á la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some special values of the parameter corresponding to r = 1, the algebra covers the cases of the su(1,1) algebra, the su(2) algebra and the ordinary Weyl-Heisenberg or oscillator algebra. For r arbitrary, the generalized Weyl-Heisenberg algebra admits finite or infinite-dimensional representations depending on the values of the parameters. Coherent states of the Perelomov type are derived in finite and infinite dimensions through a Fock-Bargmann approach based on the use of complex variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in infinite dimension. In contrast, the construction of á la Barut-Girardello coherent states in finite dimension can be achieved solely at the price to replace complex variables by generalized Grassmann variables. Finally, some preliminary developments are given for the study of Bargmann functions associated with some of the coherent states obtained in this work.

  3. Thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction

    NASA Astrophysics Data System (ADS)

    Xi, Bin; Hu, Shijie; Luo, Qiang; Zhao, Jize; Wang, Xiaoqun

    2017-01-01

    We study the thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction. This model describes the low-energy behaviors of a one-dimensional two-component bosonic model with a synthetic spin-orbit coupling in the deep insulating region. In the limit U'/U →∞ , where U is the strength of the onsite intracomponent repulsion and U' is the intercomponent one, we solve our model exactly by Jordan-Wigner transformation, and thus provide a benchmark for our following numerical approach. In other cases, we calculate the entropy and the specific heat numerically by the transfer-matrix renormalization-group method. Their low-temperature behaviors depend crucially on the properties of the zero-temperature phases. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings offer an alternative way to detect those distinguishable phases experimentally.

  4. Solving the {eta}-problem in hybrid inflation with Heisenberg symmetry and stabilized modulus

    SciTech Connect

    Antusch, Stefan; Dutta, Koushik; Kostka, Philipp M.; Bastero-Gil, Mar; King, Steve F. E-mail: mbg@ugr.es E-mail: sfk@hep.phys.soton.ac.uk

    2009-01-15

    We propose a class of models in which the {eta}-problem of supersymmetric hybrid inflation is resolved using a Heisenberg symmetry, where the associated modulus field is stabilized and made heavy with the help of the large vacuum energy during inflation without any fine-tuning. The proposed class of models is well motivated both from string theory considerations, since it includes the commonly encountered case of no-scale supergravity Kaehler potential, and from the perspective of particle physics since a natural candidate for the inflaton in this class of models is the right-handed sneutrino which is massless during the inflationary epoch, and subsequently acquires a large mass at the end of inflation. We study a specific example motivated by sneutrino hybrid inflation with no-scale supergravity in some detail, and show that the spectral index may lie within the latest WMAP range, while the tensor-to-scalar ratio is very small.

  5. Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet

    NASA Astrophysics Data System (ADS)

    Correggi, Michele; Giuliani, Alessandro; Seiringer, Robert

    2015-10-01

    We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neighbor attraction. This attractive interaction makes the lower bound on the free energy particularly tricky: the key idea there is to prove a differential inequality for the two-particle density, which is thereby shown to be smaller than the probability density of a suitably weighted two-particle random process on the lattice.

  6. Order and thermalized dynamics in Heisenberg-like square and Kagomé spin ices.

    PubMed

    Wysin, G M; Pereira, A R; Moura-Melo, W A; de Araujo, C I L

    2015-02-25

    Thermodynamic properties of a spin ice model on a Kagomé lattice are obtained from dynamic simulations and compared with properties in square lattice spin ice. The model assumes three-component Heisenberg-like dipoles of an array of planar magnetic islands situated on a Kagomé lattice. Ising variables are avoided. The island dipoles interact via long-range dipolar interactions and are restricted in their motion due to local shape anisotropies. We define various order parameters and obtain them and thermodynamic properties from the dynamics of the system via a Langevin equation, solved by the Heun algorithm. Generally, a slow cooling from high to low temperature does not lead to a particular state of order, even for a set of coupling parameters that gives well thermalized states and dynamics. At very low temperature, however, square ice is more likely to reach states near the ground state than Kagomé ice, for the same island coupling parameters.

  7. Multiple-q states and the Skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields.

    PubMed

    Okubo, Tsuyoshi; Chung, Sungki; Kawamura, Hikaru

    2012-01-06

    Ordering of the frustrated classical Heisenberg model on the triangular lattice with an incommensurate spiral structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the Skyrmion-lattice state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both Skyrmions and anti-Skyrmions, together with a new thermodynamic phase where Skyrmion and anti-Skyrmion lattices form a domain state.

  8. The four-spinon dynamical structure factor of the Heisenberg chain

    NASA Astrophysics Data System (ADS)

    Caux, Jean-Sébastien; Hagemans, Rob

    2006-12-01

    We compute the exact four-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The four-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known two-spinon part is carried by four-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.

  9. Ferrimagnetic states in S = 1/2 frustrated Heisenberg chains with period 3 exchange modulation

    NASA Astrophysics Data System (ADS)

    Hida, K.

    2007-04-01

    The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization Ms. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than Ms/3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.

  10. Renormalized entanglement in Heisenberg-Ising spin-1/2 chain with Dzyaloshinskii-Moriya interaction

    NASA Astrophysics Data System (ADS)

    Khan, Salman; Khan, Kalimullah

    2016-06-01

    The influence of the Dzyaloshinsky-Moriya (DM) interaction on entanglement in the one-dimensional spin-1/2 Heisenberg-Ising model is investigated via concurrence. The existence of two states, different in quantum properties and linked through a critical point by quantum phase transition, in the thermodynamic limit, are identified. The strong DM interaction delays quantum phase transition and hence shifts the boundary between the two phases to the region of the strong coupling constant. The increasing strength of the DM interaction strongly restores entanglement against its degradation arising from the increasing size of the system. The first derivative of the entanglement quantifier diverges to the critical point and is related directly to the divergence of the correlation length. The scaling behavior in the vicinity of the quantum critical point is also discussed.

  11. Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice.

    PubMed

    Chern, Gia-Wei; Moessner, R

    2013-02-15

    Ever since the experiments which founded the field of highly frustrated magnetism, the kagome Heisenberg antiferromagnet has been the archetypical setting for the study of fluctuation induced exotic ordering. To this day the nature of its classical low-temperature state has remained a mystery: the nonlinear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature, T. Here we present an efficient Monte Carlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations asymptote to a remarkably small value as T→0. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.

  12. Gaussian phase transition and critical exponents in spin-1 bond-alternative Heisenberg chains

    NASA Astrophysics Data System (ADS)

    Su, Yao Heng; Chen, Ai Min; Xiang, Chunhuan; Wang, Honglei; Xia, Cai-Juan; Wang, Jun

    2016-12-01

    The quantum Gaussian phase transition is investigated for the infinite spin-1 bond-alternative Heisenberg model in one spatial dimension. By using a tensor network representation with an infinite matrix product state approach, the ground state energy, bipartite entanglement entropy, non-local string order, and fidelity per lattice site are calculated to characterize the phase transition. At the quantum phase transition point, the scaling behavior of various physical observables with respect to the finite truncation dimension are discussed for the ground state wavefunctions. In addition, the central charge is extracted from the finite entanglement entropies and the finite correlation lengths. Furthermore, the various critical exponents of the string order are calculated. The characteristic critical exponents and the central charge determine the universality class of the phase transition.

  13. Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Zhang, Xiong-Peng; Shao, Bin; Zou, Jian

    2017-02-01

    Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.

  14. New insight into the thermodynamics of Heisenberg ferromagnets as inferred from high-temperature series

    NASA Astrophysics Data System (ADS)

    Kuz'min, M. D.

    2017-02-01

    In search of a suitable equation of state for ferromagnets, we revise the information about the Heisenberg model obtainable from high-temperature series. Special attention is paid to the ratio χ3 /χ4 (where χ ⁢ and ⁢χ3 are the linear and cubic susceptibilities) related to Landau's quartic coefficient b. It is found in particular that both χ3 /χ4 and b tend to a finite limit as T →TC . This limit is small - an order of magnitude smaller than predicted by Weiss's molecular field and similar theories - but contrary to the common belief, nonzero. This implies a rejection of the generally accepted critical-point exponents and a return to those of Landau: α = 0 , β = 1/2, γ = 1 , etc.

  15. Quantification of quantum discord in a antiferromagnetic Heisenberg compound

    SciTech Connect

    Singh, H. Chakraborty, T. Mitra, C.

    2014-04-24

    An experimental quantification of concurrence and quantum discord from heat capacity (C{sub p}) measurement performed over a solid state system has been reported. In this work, thermodynamic measurements were performed on copper nitrate (CN, Cu(NO{sub 3}){sub 2}⋅2.5H{sub 2}O) single crystals which is an alternating antiferromagnet Heisenberg spin 1/2 system. CN being a weak dimerized antiferromagnet is an ideal system to investigate correlations between spins. The theoretical expressions were used to obtain concurrence and quantum discord curves as a function of temperature from heat capacity data of a real macroscopic system, CN.

  16. Q-operators for the open Heisenberg spin chain

    NASA Astrophysics Data System (ADS)

    Frassek, Rouven; Szécsényi, István M.

    2015-12-01

    We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.

  17. Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet.

    PubMed

    Sandvik, Anders W

    2002-10-21

    The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.

  18. Fluctuation-dissipation ratio of the Heisenberg spin glass.

    PubMed

    Kawamura, Hikaru

    2003-06-13

    The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.

  19. Valence bond and von Neumann entanglement entropy in Heisenberg ladders.

    PubMed

    Kallin, Ann B; González, Iván; Hastings, Matthew B; Melko, Roger G

    2009-09-11

    We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.

  20. Bound States in Dimerized and Frustrated Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Bouzerar, G.; Sil, S.

    Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.

  1. Numerical study of magnetization plateaus in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice

    NASA Astrophysics Data System (ADS)

    Capponi, Sylvain

    2017-01-01

    We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaus for m =0 , 1 /4 , 1 /2 , and 3 /4 , where m is the magnetization normalized by its saturation value. These incompressible states correspond to somewhat similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m =0 . Our results are based on exact diagonalization as well as density-matrix renormalization-group large-scale simulations and interpreted in terms of simple parameter-free trial wave functions.

  2. Emergence of Long Period Antiferromagnetic Orders from Haldane Phase in S=1 Heisenberg Chains with D-Modulation

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo; Chen, Wei

    2005-07-01

    The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Néel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Néel orders. The investigation of the model with longer period D-modulation also confirms this picture.

  3. Linearized pseudo-Einstein equations on the Heisenberg group

    NASA Astrophysics Data System (ADS)

    Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard

    2017-02-01

    We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.

  4. Uncertainty in Bohr's response to the Heisenberg microscope

    NASA Astrophysics Data System (ADS)

    Tanona, Scott

    2004-09-01

    In this paper, I analyze Bohr's account of the uncertainty relations in Heisenberg's gamma-ray microscope thought experiment and address the question of whether Bohr thought uncertainty was epistemological or ontological. Bohr's account seems to allow that the electron being investigated has definite properties which we cannot measure, but other parts of his Como lecture seem to indicate that he thought that electrons are wave-packets which do not have well-defined properties. I argue that his account merges the ontological and epistemological aspects of uncertainty. However, Bohr reached this conclusion not from positivism, as perhaps Heisenberg did, but because he was led to that conclusion by his understanding of the physics in terms of nonseparability and the correspondence principle. Bohr argued that the wave theory from which he derived the uncertainty relations was not to be taken literally, but rather symbolically, as an expression of the limited applicability of classical concepts to parts of entangled quantum systems. Complementarity and uncertainty are consequences of the formalism, properly interpreted, and not something brought to the physics from external philosophical views.

  5. Relation of the nonlinear Heisenberg algebras in two dimensions with linear ones

    NASA Astrophysics Data System (ADS)

    Chung, Won Sang

    2015-07-01

    In this paper, we discuss the relation of the nonlinear Heisenberg algebras in two dimensions with linear ones following the Nowicki and Tkachuk's approach for one-dimensional case. For one-dimensional harmonic oscillator, we obtain the solution explicitly. For the nonlinear Heisenberg algebras in two dimensions, we introduce two generators to transform this algebra into the linear one. For the linear version of the nonlinear Heisenberg algebras in two dimensions, we obtain the eigenfunction for the position and angular momentum operator and solve the harmonic oscillator problem in two dimensions.

  6. Pauli-Heisenberg Oscillations in Electron Quantum Transport.

    PubMed

    Thibault, Karl; Gabelli, Julien; Lupien, Christian; Reulet, Bertrand

    2015-06-12

    We measure the current fluctuations emitted by a normal-metal-insulator-normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature T=35  mK. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.

  7. Experimental estimation of discord in an antiferromagnetic Heisenberg compound

    NASA Astrophysics Data System (ADS)

    Singh, H.; Chakraborty, T.; Panigrahi, P. K.; Mitra, C.

    2015-03-01

    Temperature-dependent static magnetic susceptibility and heat capacity data were employed to quantify quantum discord in copper nitrate which is a spin 1/2 antiferromagnetic Heisenberg system. With the help of existing theoretical formulations, quantum discord, mutual information, and purely classical correlation were estimated as a function of temperature using the experimental data. The experimentally quantified correlations estimated from susceptibility and heat capacity data are consistent with each other, and they exhibit a good match with theoretical predictions. Violation of Bell's inequality was also checked using the static magnetic susceptibility as well as heat capacity data. Quantum discord estimated from magnetic susceptibility as well as heat capacity data is found to be present in the thermal states of the system even when the system is in a separable state.

  8. Heisenberg-limited atom clocks based on entangled qubits.

    PubMed

    Kessler, E M; Kómár, P; Bishof, M; Jiang, L; Sørensen, A S; Ye, J; Lukin, M D

    2014-05-16

    We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.

  9. Werner Heisenberg zum 100. Geburtstag: Pionier der Quantenmechanik

    NASA Astrophysics Data System (ADS)

    Jacobi, Manfred

    2001-11-01

    Werner Heisenberg war eine der prägendsten Gestalten der Physik des 20. Jahrhunderts. Zu seinen wichtigsten Verdiensten gehören die Grundlegung der Quantenmechanik, die Formulierung der Unschärferelationen sowie die Beteiligung an der Ausarbeitung der Kopenhagener Deutung der Quantenmechanik. Darüber hinaus lieferte er Arbeiten von fundamentalem Charakter zur Theorie des Atomkerns, zur kosmischen Strahlung und zur Quantenfeldtheorie. Während des Krieges war er an den Arbeiten des Uranvereins beteiligt, der die Möglichkeit einer Entwicklung von Kernwaffen untersuchte, jedoch über Vorarbeiten zur Reaktorphysik nicht hinauskam. Wegen dieser Tätigkeit wurde er bei Kriegsende für einige Monate in England interniert. Nach seiner Rückkehr widmete er sich vor allem dem Aufbau der Physik in Deutschland, die während der NS-Zeit nahezu ihrer gesamten Substanz beraubt worden war.

  10. Quantum spin transistor with a Heisenberg spin chain

    PubMed Central

    Marchukov, O. V.; Volosniev, A. G.; Valiente, M.; Petrosyan, D.; Zinner, N. T.

    2016-01-01

    Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements. PMID:27721438

  11. Distribution of NMR relaxations in a random Heisenberg chain.

    PubMed

    Shiroka, T; Casola, F; Glazkov, V; Zheludev, A; Prša, K; Ott, H-R; Mesot, J

    2011-04-01

    NMR measurements of the (29)Si spin-lattice relaxation time T(1) were used to probe the spin-1/2 random Heisenberg chain compound BaCu(2)(Si(1-x)Ge(x))(2)O(7). Remarkable differences between the pure (x=0) and the fully random (x=0.5) cases are observed, indicating that randomness generates a distribution of local magnetic relaxations. This distribution, which is reflected in a stretched exponential NMR relaxation, exhibits a progressive broadening with decreasing temperature, caused by a growing inequivalence of magnetic sites. Compelling independent evidence for the influence of randomness is also obtained from magnetization data and Monte Carlo calculations. These results suggest the formation of random-singlet states in this class of materials, as previously predicted by theory.

  12. Fitting magnetic field gradient with Heisenberg-scaling accuracy

    PubMed Central

    Zhang, Yong-Liang; Wang, Huan; Jing, Li; Mu, Liang-Zhu; Fan, Heng

    2014-01-01

    The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements. PMID:25487218

  13. Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets

    DOE PAGES

    Johnston, David C.

    2015-02-27

    In this study, a unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility χ versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions Jij between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θp in the Curie-Weiss law is written in terms of the Jij values and TNmore » in terms of the Jij values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S. For collinear ordering these properties are the reduced temperature t=T/TN, the ratio f = θp/TN, and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ(T ≤ TN) of noncollinear 120° spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S, and the reduced perpendicular field versus reduced temperature phase diagram is constructed.« less

  14. Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets

    SciTech Connect

    Johnston, David C.

    2015-02-27

    In this study, a unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility χ versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions Jij between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θp in the Curie-Weiss law is written in terms of the Jij values and TN in terms of the Jij values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S. For collinear ordering these properties are the reduced temperature t=T/TN, the ratio f = θp/TN, and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ(T ≤ TN) of noncollinear 120° spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S, and the reduced perpendicular field versus reduced temperature phase diagram is constructed.

  15. The Heisenberg-Euler Lagrangian as an example of an effective field theory

    NASA Astrophysics Data System (ADS)

    Dittrich, Walter

    2014-10-01

    We review the beginning of the effective Lagrangian in QED that was first introduced in the literature by W. Heisenberg and H. Euler in 1936. Deviating from their way of calculating the one-loop effective correction to the classical Maxwell Lagrangian, we use Green's functions and adopt the Fock-Schwinger proper-time method. The important role of the Heisenberg-Euler effective Lagrangian is explicitly demonstrated for low-energy photon-photon processes.

  16. Werner Heisenberg and Carl Friedrich Freiherr von Weizsäcker: A Fifty-Year Friendship*

    NASA Astrophysics Data System (ADS)

    Cassidy, David C.

    2015-03-01

    This paper follows Werner Heisenberg and Carl Friedrich von Weizsäcker during their fifty-year friendship from 1926, when they first met in Copenhagen, to Heisenberg's death in Munich in 1976. The relationship underwent profound changes during that period, as did physics, philosophy, and German society and politics, all of which exerted important influences on their lives, work, and interactions with each other. The nature of these developments and their impact are explored in this paper.

  17. Adiabatic demagnetization of the antiferromagnetic spin-1/2 Heisenberg hexagonal cluster

    NASA Astrophysics Data System (ADS)

    Deb, Moumita; Ghosh, Asim Kumar

    2016-05-01

    Exact analytic expressions of eigenvalues of the antiferromagnetic spin-1/2 Heisenberg hexagon in the presence of uniform magnetic field have been obtained. Magnetization process, nature of isentrops and properties of magneto caloric effect in terms of adiabatic demagnetization have been investigated. Theoretical results have been used to study the magneto caloric effect of the spin-1/2 Heisenberg hexagonal compound Cu3WO6.

  18. Edge magnetism of Heisenberg model on honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau

    2017-03-01

    Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.

  19. Edge magnetism of Heisenberg model on honeycomb lattice.

    PubMed

    Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau

    2017-03-07

    Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.

  20. Edge magnetism of Heisenberg model on honeycomb lattice

    PubMed Central

    Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau

    2017-01-01

    Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials. PMID:28266559

  1. Electromagnetic Fields on Time-Involute Particles Around Biharmonic Particles and its Lorentz Transformations in Heisenberg Spacetime

    NASA Astrophysics Data System (ADS)

    Körpinar, Talat; Asi˙l, Vedat; Turhan, Essin

    2015-01-01

    In this paper, we obtain the new parametric representation for a time-involute particles in Heisenberg spacetime . By using the Frenet frame, we derive the necessary and sufficient conditions to construct a biharmonic particle Heisenberg spacetime . We give a geometrical description of time-involute particles around timelike biharmonic particle in . Moreover, we obtain Lorentz transformations this particles. Finally, we give the relationship of electromagnetic fields on Heisenberg spacetime.

  2. Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice

    NASA Astrophysics Data System (ADS)

    Chern, Gia-Wei

    2014-03-01

    The first experiments on the ``kagome bilayer'' SCGO triggered a wave of interest in kagome antiferromagnets in particular, and frustrated systems in general. A cluster of early seminal theoretical papers established kagome magnets as model systems for novel ordering phenomena, discussing in particular spin liquidity, partial order, disorder-free glassiness and order by disorder. Despite significant recent progress in understanding the ground state for the quantum S = 1 / 2 model, the nature of the low-temperature phase for the classical kagome Heisenberg antiferromagnet has remained a mystery: the non-linear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature. Here we present an efficient Monte Carlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations saturate at a remarkably small value. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.

  3. Quantum phase transitions in the Heisenberg J1-J2 triangular antiferromagnet in a magnetic field

    NASA Astrophysics Data System (ADS)

    Ye, Mengxing; Chubukov, Andrey V.

    2017-01-01

    We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1 and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin S , for J2/J1<1 /8 , quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0 , and for 1 /8 model with arbitrary S , including S =1 /2 , near the saturation field by exploring the fact that near saturation the density of bosons is small for all S . We show that for S >1 , the transition remains first order, with a finite hysteresis width, but for S =1 /2 and, possibly, S =1 , there appears a new intermediate phase without a quasiclassical long-range order.

  4. Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

    NASA Astrophysics Data System (ADS)

    Karrasch, C.

    2017-03-01

    We illustrate how finite-temperature charge and thermal Drude weights of one-dimensional systems can be obtained from the relaxation of initial states featuring global (left–right) gradients in the chemical potential or temperature. The approach is tested for spinless interacting fermions as well as for the Fermi-Hubbard model, and the behavior in the vicinity of special points (such as half filling or isotropic chains) is discussed. We present technical details on how to implement the calculation in practice using the density matrix renormalization group and show that the non-equilibrium dynamics is often less demanding to simulate numerically and features simpler finite-time transients than the corresponding linear response current correlators; thus, new parameter regimes can become accessible. As an application, we determine the thermal Drude weight of the Hubbard model for temperatures T which are an order of magnitude smaller than those reached in the equilibrium approach. This allows us to demonstrate that at low T and half filling, thermal transport is successively governed by spin excitations and described quantitatively by the Bethe ansatz Drude weight of the Heisenberg chain.

  5. Heisenberg scaling of time-limited quantum metrology with realistic decoherence

    NASA Astrophysics Data System (ADS)

    Hardy, Maxime; Coish, William A.

    2012-02-01

    The prospect of using entanglement to improve various metrology tasks is one of the most promising avenues for a near-term real-world benefit from genuine quantum phenomena [1]. However, in the standard scenario, history-independent Markovian dephasing removes the quantum advantage [2]. We revisit the problem of quantum metrology using the model of trapped ions subject to non-Markovian phase damping decoherence caused by Gaussian noise with finite correlation length and time (a slight generalization of the model used in Ref. [3]). Assuming a fixed available measurement time shorter than the noise correlation time (the non-Markovian limit) and a noise source that is local in space, we recover Heisenberg scaling (˜1/N). This allows one to measure an ``instantaneous'' frequency to a higher precision than the time-averaged noise amplitude and moreover to a higher precision than classically allowed. Interestingly, for this protocol we show that the optimal number of measurements to be performed within the measurement time is three. [4pt] [1] V. Giovannetti, S. Lloyd, and L. Maccone Nature Photonics 5, 222 (2011) [2] S. F. Huelga et al. Phys. Rev. Lett. 79, 3865 (1997 [3] T. Monz et al. Phys. Rev. Lett. 106, 130506 (2011)

  6. Experimental optical phase measurement at the exact Heisenberg limit (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Daryanoosh, Shakib; Slussarenko, Sergei; Wiseman, Howard M.; Pryde, Geoff J.

    2016-10-01

    Optical phase measurement through its application in quantum metrology has pushed the precision limit with which some physical quantities can be measured accurately. At the very fundamental level, the laws of quantum mechanics dictate that the uncertainty in phase estimations scales as 1/N, where N is the number of quantum resources employed in the protocol [1]. This is the well known Heisenberg limit (HL) which is quadratically better than the traditional precision limit known as the standard quantum limit (SQL) with uncertainty asymptotically scaling as 1/&sqrt{N} [1]. Several experiments have demonstrated that the SQL can be beaten by using an entangled state as the probe and a specific measurement scheme for ab initio estimation of unknown phases [2,3]. It has also been shown experimentally that even in the absence of the entanglement one can measure an unknown phase with imprecision scaling at the HL [4]. In this work we first present a new protocol able to estimate an optical phase at the Heisenberg limit, and then experimentally explore fundamental and practical issues in generating high-quality novel entangled states, for use in this protocol and beyond. Our aim in this study is to measure an unknown phase in the interval [0,2π) with uncertainty attaining the exact HL. There is a condition that should be met to address this objective: preparation of an optimal state [5]. This would cover part of the presentation through which we explain how to experimentally realise such an optimal state with the current technological limitations and the feasibility of the scheme. In particular, we generate an entangled 3-photon (2-photon) state of specific superposition of GHZ (Bell) states. Our numerical simulation of the phase measurement gate together with the experimental outcomes show that the created state should have a high fidelity and purity to be able to have the phase uncertainty achieving the exact HL. Therefore, we briefly explain the modelling for

  7. Critical dynamics of the classical anisotropic BCC Heisenberg antiferromagnet.

    NASA Astrophysics Data System (ADS)

    Tsai, Shan-Ho; Bunker, Alex; Landau, D. P.

    2001-03-01

    Large-scale spin-dynamics simulations have been used to investigate the dynamic behavior of the classical Heisenberg antiferromagnet with single-site uniaxial anisotropy, in bcc lattices. Time evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using an algorithm implemented by Krech et al [1], which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor S(q,ω) was calculated from the space- and time-displaced spin-spin correlation function. Preliminary results for the transverse and the longitudinal components of S(q,ω) show that while the former is propagative, with a relatively short time scale, the latter is diffusive and its computation requires very long time integrations. Because of difficulties for experiments to probe the critical region, experimental data have not yet been able to distinguish between competing theories. While limited by finite lattice size and finite integration time, simulations offer the hope of shedding light on the differences between theories and experiment. [1] M. Krech, A. Bunker, D.P. Landau, Comput. Phys. Commun. 111, 1 (1998). Supported by NSF and SDSC

  8. Excited state correlations of the finite Heisenberg chain

    NASA Astrophysics Data System (ADS)

    Pozsgay, Balázs

    2017-02-01

    We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator < σ 1zσ 2z> , which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBA-like description for the building blocks of the construction.

  9. Soft Heisenberg hair on black holes in three dimensions

    NASA Astrophysics Data System (ADS)

    Afshar, Hamid; Detournay, Stephane; Grumiller, Daniel; Merbis, Wout; Perez, Alfredo; Tempo, David; Troncoso, Ricardo

    2016-05-01

    Three-dimensional Einstein gravity with a negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near-horizon region of these black holes that lead to a surprisingly simple near-horizon symmetry algebra consisting of two affine u ^(1 ) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-Hawking entropy of Bañados-Teitelboim-Zanelli black holes and "black flower" generalizations. From the near-horizon perspective the conformal generators at asymptotic infinity appear as composite operators, which we interpret in the spirit of black hole complementarity. Another remarkable feature of our boundary conditions is that they are singled out by requiring that the whole spectrum is compatible with regularity at the horizon, regardless of the value of the global charges like mass or angular momentum. Finally, we address black hole microstates and generalizations to cosmological horizons.

  10. Spin dynamics and magnetic correlation length in two-dimensional quantum heisenberg antiferromagnets

    PubMed

    Carretta; Ciabattoni; Cuccoli; Mognaschi; Rigamonti; Tognetti; Verrucchi

    2000-01-10

    The correlated spin dynamics and temperature dependence of the correlation length xi(T) in two-dimensional quantum (S = 1/2) Heisenberg antiferromagnets (2DQHAF) on a square lattice are discussed in light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate. In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La2CuO4 and Sr2CuO2Cl2. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out to be in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of xi(T) is in agreement with high-temperature expansions, quantum Monte Carlo simulations, and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the nonlinear sigma model, no evidence of crossover between different quantum regimes is observed.

  11. Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings

    NASA Astrophysics Data System (ADS)

    Casa Grande, H. L.; Laflorencie, N.; Alet, F.; Vieira, A. P.

    2014-04-01

    We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta, and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.

  12. Semiclassical initial value representation for the quantum propagator in the Heisenberg interaction representation

    SciTech Connect

    Petersen, Jakob; Pollak, Eli

    2015-12-14

    One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler and cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the “standard” SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk’s frozen Gaussian and Heller’s thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.

  13. Semiclassical initial value representation for the quantum propagator in the Heisenberg interaction representation

    NASA Astrophysics Data System (ADS)

    Petersen, Jakob; Pollak, Eli

    2015-12-01

    One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler and cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the "standard" SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk's frozen Gaussian and Heller's thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.

  14. Metastable minima of the Heisenberg spin glass in a random magnetic field

    NASA Astrophysics Data System (ADS)

    Sharma, Auditya; Yeo, Joonhyun; Moore, M. A.

    2016-11-01

    We have studied zero-temperature metastable minima in classical m -vector component spin glasses in the presence of m -component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for m >2 . We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the m =2 and m =3 cases in the SK model the final energy reached in the quench is very close to the energy Ec at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states ρ (λ ) of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual √{λ } form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.

  15. Off the Beat. An Appreciation of Werner Heisenberg and Some Talk About How Physics Was in the Good Old Days

    ERIC Educational Resources Information Center

    Thomsen, Dietrick E.

    1976-01-01

    Presented is an insight into man's idea about physics and being a physicist in the days when Heisenberg, P. A. M. Dirac, Louis de Broglic and other famous physicists were young men. Heisenberg is compared to Newton, inventing new math as he needed it. Emphasis is placed on the fact that he was not a Nazi sympathizer. (EB)

  16. Energy spectrum of the two-magnon bound states in the Heisenberg-Ising antiferromagnet on the square lattice

    NASA Astrophysics Data System (ADS)

    Hamer, C. J.

    2009-06-01

    The energy spectra of the two-magnon bound states in the Heisenberg-Ising antiferromagnet on the square lattice are calculated using series expansion methods. The results confirm an earlier spin-wave prediction of Oguchi and Ishikawa that the bound states vanish into the continuum before the isotropic Heisenberg limit is reached.

  17. Magnetization Process and Magnetocaloric Effect of the Spin-1/2 XXZ Heisenberg Cuboctahedron

    NASA Astrophysics Data System (ADS)

    Karľová, Katarína; Strečka, Jozef

    2016-10-01

    Magnetic properties of the spin-1/2 XXZ Heisenberg cuboctahedron are examined using exact numerical diagonalization depending on a relative strength of the exchange anisotropy. While the Ising cuboctahedron exhibits in a low-temperature magnetization curve only one-third magnetization plateau, the XXZ Heisenberg cuboctahedron displays another four intermediate plateaux at zero, one-sixth, one-half and two-thirds of the saturation magnetization. The novel magnetization plateaux generally extend over a wider range of magnetic fields with increasing of a quantum (xy) part of the XXZ exchange interaction. It is shown that the XXZ Heisenberg cuboctahedron exhibits in the vicinity of all magnetization jumps anomalous thermodynamic behavior accompanied by an enhanced magnetocaloric effect.

  18. Near-Heisenberg-limited atomic clocks in the presence of decoherence.

    PubMed

    Borregaard, J; Sørensen, A S

    2013-08-30

    The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near-Heisenberg-limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence.

  19. Violation of Heisenberg's error-disturbance uncertainty relation in neutron-spin measurements

    NASA Astrophysics Data System (ADS)

    Sulyok, Georg; Sponar, Stephan; Erhart, Jacqueline; Badurek, Gerald; Ozawa, Masanao; Hasegawa, Yuji

    2013-08-01

    In its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments have turned out to be correct only for special cases. An alternative universally valid relation was derived by Ozawa in 2003. Here, we demonstrate that Ozawa's predictions hold for projective neutron-spin measurements. The experimental inaccessibility of error and disturbance claimed elsewhere has been overcome using a tomographic method. By a systematic variation of experimental parameters in the entire configuration space, the physical behavior of error and disturbance for projective spin-(1)/(2) measurements is illustrated comprehensively. The violation of Heisenberg's original relation, as well as the validity of Ozawa's relation become manifest. In addition, our results conclude that the widespread assumption of a reciprocal relation between error and disturbance is not valid in general.

  20. Synthesis and characterization of the new two-dimensional Heisenberg antiferromagnet double perovskite BaLaCuSbO6.

    PubMed

    Blanco, M Cecilia; Paz, Sergio Alexis; Nassif, Vivian M; Guimpel, Julio J; Carbonio, Raúl E

    2015-06-21

    The BaLaCuSbO(6) double perovskite has been successfully synthesized by solid state reaction under an air atmosphere. Its structure was refined using powder neutron diffraction in the monoclinic space group I2/m with a 4% antisite disorder on the B cations. Magnetic measurements give signs of 2D-antiferromagnetic behaviour with TN around 64 K. The Jahn-Teller distortion produced by Cu(2+) ions favours a crystallographic tetragonal distortion and consequently the in-plane super-superexchange antiferromagnetic interactions, J(90°), are favoured over the in-plane J(180°) antiferromagnetic exchange interactions. Both, J and J' magnetic interactions have been evaluated according to a Heisenberg antiferromagnetic rectangular model using an approximation to Curie's law in powers of J/T, being |J| around 10 times stronger than |J'|.

  1. Exotic Ground State Phases of S=1/2 Heisenberg Δ-Chain with Ferromagnetic Main Chain

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2008-04-01

    The ground state phase diagram of the spin-1/2 Heisenberg frustrated Δ-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.

  2. Giant spin gap and magnon localization in the disordered Heisenberg antiferromagnet Sr2Ir1 -xRuxO4

    NASA Astrophysics Data System (ADS)

    Cao, Yue; Liu, X.; Xu, Wenhu; Yin, Wei-Guo; Meyers, D.; Kim, Jungho; Casa, Diego; Upton, M. H.; Gog, Thomas; Berlijn, Tom; Alvarez, Gonzalo; Yuan, Shujuan; Terzic, Jasminka; Tranquada, J. M.; Hill, John P.; Cao, Gang; Konik, Robert M.; Dean, M. P. M.

    2017-03-01

    We study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1 -xRuxO4 . The maximum energy of the magnetic excitation remains robust up to x =0.77 , with a gap opening at low dopings and increasing to over 150 meV at x =0.77 . At these higher Ru concentrations, the dispersive magnetic excitations in Sr2IrO4 are rendered essentially momentum independent. Up to a Ru concentration of x =0.77 , both experiments and first-principles calculations show the Ir Jeff=1 /2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder. Under the coherent potential approximation, we reproduce the experimental magnetic excitations using the disordered Heisenberg antiferromagnetic model with suppressed next-nearest-neighbor ferromagnetic coupling.

  3. Giant spin gap and magnon localization in the disordered Heisenberg antiferromagnet Sr2Ir1-xRuxO4

    DOE PAGES

    Cao, Yue; Liu, X.; Xu, Wenhu; ...

    2017-03-06

    Here, we study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1–xRuxO4. The maximum energy of the magnetic excitation remains robust up to x = 0.77, with a gap opening at low dopings and increasing to over 150 meV at x = 0.77. At these higher Ru concentrations, the dispersive magnetic excitations in Sr2IrO4 are rendered essentially momentum independent. Up to a Ru concentration of x = 0.77, both experiments and first-principles calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder.more » Under the coherent potential approximation, we reproduce the experimental magnetic excitations using the disordered Heisenberg antiferromagnetic model with suppressed next-nearest-neighbor ferromagnetic coupling.« less

  4. Heisenberg-limited interferometry with pair coherent states and parity measurements

    SciTech Connect

    Gerry, Christopher C.; Mimih, Jihane

    2010-07-15

    After reviewing parity-measurement-based interferometry with twin Fock states, which allows for supersensitivity (Heisenberg limited) and super-resolution, we consider interferometry with two different superpositions of twin Fock states, namely, two-mode squeezed vacuum states and pair coherent states. This study is motivated by the experimental challenge of producing twin Fock states on opposite sides of a beam splitter. We find that input two-mode squeezed states, while allowing for Heisenberg-limited sensitivity, do not yield super-resolutions, whereas both are possible with input pair coherent states.

  5. Spin liquid nature in the Heisenberg J1-J2 triangular antiferromagnet

    NASA Astrophysics Data System (ADS)

    Iqbal, Yasir; Hu, Wen-Jun; Thomale, Ronny; Poilblanc, Didier; Becca, Federico

    2016-04-01

    We investigate the spin-1/2 Heisenberg model on the triangular lattice in the presence of nearest-neighbor J1 and next-nearest-neighbor J2 antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015), 10.1103/PhysRevB.92.041105 and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015), 10.1103/PhysRevB.92.140403], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime 0.08 ≲J2/J1≲0.16 , framed by 120∘ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) J2/J1 . By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless U(1 ) Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped Z2 spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.

  6. Bond Operator Mean Field Approach to the Magnetization Plateaux in Quantum Antiferromagnets —Application to the S=1/2 Coupled Dimerized Zigzag Heisenberg Chains—

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo; Shiino, Masaru; Chen, Wei

    2004-06-01

    The magnetization plateaux in two dimensionally coupled S=1/2 dimerized zigzag Heisenberg chains are investigated by means of the bond operator mean field approximation. In the absence of the interchain coupling, this model is known to have a plateau at half of the saturation magnetization accompanied by the spontaneous translational symmetry breakdown. The parameter regime in which the plateau appears is reproduced well within the present approximation. In the presence of the interchain coupling, this plateau is shown to be suppressed. This result is also supported by the numerical diagonalization calculation.

  7. Chern-Simons theory of the anisotropic quantum Heisenberg antiferromagnet on a square lattice

    SciTech Connect

    Lopez, A. ); Rojo, A.G. Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120 ); Fradkin, E. )

    1994-06-01

    We consider the anisotropic quantum Heisenberg antiferromagnetic (with anistropy [lambda]) on a square lattice using a Chern-Simons (or Wigner-Jordan) approach. We show that the average field approximation (AFA) yields a phase diagram with two phases: a Neel state for [lambda][gt][lambda][sub [ital c

  8. Exact Baker–Campbell–Hausdorff formula for the contact Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Bravetti, Alessandro; Garcia-Chung, Angel; Tapias, Diego

    2017-03-01

    In this work we introduce the contact Heisenberg algebra which is the restriction of the Jacobi algebra on contact manifolds to the linear and constant functions. We give the exact expression of its corresponding Baker–Campbell–Hausdorff formula. We argue that this result is relevant to the quantization of contact systems.

  9. Studying the thermally entangled state of a three-qubit Heisenberg XX ring via quantum teleportation

    SciTech Connect

    Yeo, Ye

    2003-08-01

    We consider quantum teleportation as a tool to investigate the thermally entangled state of a three-qubit Heisenberg XX ring. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very different average teleportation fidelities.

  10. Phase diagram of a three-sublattice mixed ferro-ferrimagnetic Heisenberg system

    NASA Astrophysics Data System (ADS)

    Mert, H. Şevki; Mert, Gülistan

    2013-10-01

    We present a numerical study of a three-sublattice mixed ferro-ferrimagnetic Heisenberg system. Green's function technique is used to calculate the magnetization as a function of temperature. The technique involves the random phase approximation and Anderson-Callen's decoupling. We obtain phase diagram and the first-order phase transition.

  11. While Heisenberg Is Not Looking: The Strength of "Weak Measurements" in Educational Research

    ERIC Educational Resources Information Center

    Geelan, David R.

    2015-01-01

    The concept of "weak measurements" in quantum physics is a way of "cheating" the Uncertainty Principle. Heisenberg stated (and 85 years of experiments have demonstrated) that it is impossible to know both the position and momentum of a particle with arbitrary precision. More precise measurements of one decrease the precision…

  12. The Taylor spectrum and transversality for a Heisenberg algebra of operators

    SciTech Connect

    Dosi, Anar A

    2010-05-11

    A problem on noncommutative holomorphic functional calculus is considered for a Banach module over a finite-dimensional nilpotent Lie algebra. As the main result, the transversality property of algebras of noncommutative holomorphic functions with respect to the Taylor spectrum is established for a family of bounded linear operators generating a Heisenberg algebra. Bibliography: 25 titles.

  13. Permutation-parity exchange at a beam splitter: Application to Heisenberg-limited interferometry

    SciTech Connect

    Campos, Richard A.; Gerry, Christopher C.

    2005-12-15

    Quantum-optical permutation and parity observables are unitarily exchanged by a 50:50 beam splitter. Bosonic coalescence effects are reexamined from this point of view. We show that photon-number resolving counters behind a beam splitter define a permutation detector for the input optical field. With suitable phase encoding, the detector also enables Heisenberg-limited interferometry.

  14. Interaction-based quantum metrology showing scaling beyond the Heisenberg limit.

    PubMed

    Napolitano, M; Koschorreck, M; Dubost, B; Behbood, N; Sewell, R J; Mitchell, M W

    2011-03-24

    Quantum metrology aims to use entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the standard quantum limit of sensitivity, δχ ∝ N(-1/2). However, using N entangled particles and exotic states, such an interferometer can in principle achieve the Heisenberg limit, δχ ∝ N(-1). Recent theoretical work has argued that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N(-k) with appropriate entangled states and δχ ∝ N(-(k-1/2)) even without entanglement. Here we demonstrate 'super-Heisenberg' scaling of δχ ∝ N(-3/2) in a nonlinear, non-destructive measurement of the magnetization of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (corresponding to k = 2) while preserving quantum-noise-limited performance. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large numbers by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other situations, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship between scaling and sensitivity in nonlinear systems. Our work shows that interparticle interactions can improve sensitivity in a quantum-limited measurement, and experimentally demonstrates a new resource for quantum metrology.

  15. Paramagnetic susceptibility and correlation functions of a d-dimensional classical Heisenberg ferromagnet via the two-time Green function method

    NASA Astrophysics Data System (ADS)

    Campana, L. S.; Cavallo, A.; Cesare, L. De; Esposito, U.; Naddeo, A.

    2017-04-01

    In the present paper we investigate the paramagnetic susceptibility and the short-range order correlation functions of a d-dimensional classical isotropic ferromagnetic Heisenberg model with short-range exchange interactions by employing the two-time Green function method in classical statistical mechanics. Here we use Tyablikov-Callen-like decouplings for higher order Green functions and a formula for magnetization recently obtained by extension of the well known Callen method developed many years ago for the quantum isotropic Heisenberg model. Although our analysis is true for any temperature and dimensionality, we focus on one-, and some two- and three-dimensional lattices of experimental interest and derive asymptotic expressions for susceptibility and correlation functions within the paramagnetic phase close to the phase boundary and in the high-temperature regime. Besides, we present a Fourier series expansion method for deriving the high-temperature behaviors of the correlation functions. Our predictions, as obtained from a genuine classical many-body framework, may constitute a good reference point for the quantum counterparts emerging in the classical limit at the same level of approximation. Of course, although the classical spin models have unrealistic properties at sufficiently low temperatures, our classical analysis provides, in a relatively simple way as compared to a quantum treatment, an experimentally interesting scenario at finite temperature and dimensionalities d ≥ 1.

  16. Entangling qubits by Heisenberg spin exchange and anyon braiding

    NASA Astrophysics Data System (ADS)

    Zeuch, Daniel

    As the discovery of quantum mechanics signified a revolution in the world of physics more than one century ago, the notion of a quantum computer in 1981 marked the beginning of a drastic change of our understanding of information and computability. In a quantum computer, information is stored using quantum bits, or qubits, which are described by a quantum-mechanical superposition of the quantum states 0 and 1. Computation then proceeds by acting with unitary operations on these qubits. These operations are referred to as quantum logic gates, in analogy to classical computation where bits are acted on by classical logic gates. In order to perform universal quantum computation it is, in principle, sufficient to carry out single-qubit gates and two-qubit gates, where the former act on individual qubits and the latter, acting on two qubits, are used to entangle qubits with each other. The present thesis is divided into two main parts. In the first, we are concerned with spin-based quantum computation. In a spin-based quantum computer, qubits are encoded into the Hilbert space spanned by spin-1/2 particles, such as electron spins trapped in semiconductor quantum dots. For a suitable qubit encoding, turning on-and-off, or "pulsing,'' the isotropic Heisenberg exchange Hamiltonian JSi · Sj allows for universal quantum computation and it is this scheme, known as exchange-only quantum computation, which we focus on. In the second part of this thesis, we consider a topological quantum computer in which qubits are encoded using so-called Fibonacci anyons, exotic quasiparticle excitations that obey non-Abelian statistics, and which may emerge in certain two-dimensional topological systems such as fractional quantum-Hall states. Quantum gates can then be carried out by moving these particles around one another, a process that can be viewed as braiding their 2+1 dimensional worldlines. The subject of the present thesis is the development and theoretical understanding of

  17. Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements

    NASA Astrophysics Data System (ADS)

    Campos, R. A.; Gerry, Christopher C.; Benmoussa, A.

    2003-08-01

    Holland and Burnett [Phys. Rev. Lett. 71, 1355 (1993)] have argued that twin Fock states of equal photon number N injected at both input ports of a Mach-Zehnder interferometer lead to phase measurements with accuracies approaching the Heisenberg limit ΔφHL=1/(2N). However, the method of phase detection suggested by those authors, obtaining the difference of the photocurrents at the output ports of the interferometer, is not sensitive to the phase difference between the two interferometer paths; in fact, the photocurrent vanishes. In this paper we show that the use of parity measurements on just one of the output modes not only is sensitive to the phase difference but that the sensitivity approaches the Heisenberg limit for large N.

  18. Observability, Anschaulichkeit and Abstraction: A Journey into Werner Heisenberg's Science and Philosophy

    NASA Astrophysics Data System (ADS)

    Lacki, Jan

    2003-09-01

    Werner Heisenberg was one of the greatest physicists of the 20th century. He participated as a front rank actor in the shaping of a good part of XXth century physics and directly witnessed most of the intellectual struggles which led to what he called “Wandlungen in den Grundlagen der exakten Naturwissenschaft”. This expression is borrowed from one of the many talks and writings he devoted to the analysis of the scientific and philosophical implications of his, and his fellows physicists, findings. Indeed, Heisenberg's scientific activity increasingly reflected his more general intellectual views. This makes him another magnificent representative of a glorious linage going from the remote times of modern science to Einstein, Bohr and the like. This “philosophical” vein started early in his scientific life, and got stronger with time, prompted by the highly demanding scientific, but also social and political context of his mature years.

  19. Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet

    DOE PAGES

    Fu, Mingxuan; Imai, Takahashi; Han, Tian -Heng; ...

    2015-11-06

    Here, the kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χkagome, deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with themore » magnetic field dependence of χkagome that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.« less

  20. Three-qubit thermal entanglement via entanglement swapping on two-qubit Heisenberg XY chains

    SciTech Connect

    Kao, Zi Chong; Ng, Jezreel; Yeo, Ye

    2005-12-15

    In this paper, we consider the generation of a three-qubit Greenberger-Horne-Zeilinger-like thermal state by applying the entanglement swapping scheme of Zukowski et al. [Ann. N. Y. Acad. Sci. 755, 91 (1995)] to three pairs of two-qubit Heisenberg XY chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson et al. [Phys. Rev. A 58, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we are still able to achieve nonclassical fidelities for the anisotropic Heisenberg XY chains at finitely higher and higher temperatures by adjusting the strengths of an external magnetic field. This has a positive implication on the solid-state realization of a quantum computer.

  1. The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

    NASA Astrophysics Data System (ADS)

    Masood, Syed; Faizal, Mir; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B.

    2016-12-01

    In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.

  2. Aharonov-Bohm effect in quantum-to-classical correspondence of the Heisenberg principle

    SciTech Connect

    Lin, D.-H.; Chang, J.-G.; Hwang, C.-C.

    2003-04-01

    The exact energy spectrum and wave function of a charged particle moving in the Coulomb field and Aharonov-Bohm's magnetic flux are solved by the nonintegrable phase factor. The universal formula for the matrix elements of the radial operator r{sup {alpha}} of arbitrary power {alpha} is given by an analytical solution. The difference between the classical limit of matrix elements of inverse radius in quantum mechanics and the Fourier components of the corresponding quantity for the pure Coulomb system in classical mechanics is examined in reference to the correspondence principle of Heisenberg. Explicit calculation shows that the influence of nonlocal Aharonov-Bohm effect exists even in the classical limit. The semiclassical quantization rule for systems containing the topological effect is presented in the light of Heisenberg's corresponding principle.

  3. Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements

    SciTech Connect

    Campos, R. A.; Gerry, Christopher C.; Benmoussa, A.

    2003-08-01

    Holland and Burnett [Phys. Rev. Lett. 71, 1355 (1993)] have argued that twin Fock states of equal photon number N injected at both input ports of a Mach-Zehnder interferometer lead to phase measurements with accuracies approaching the Heisenberg limit {delta}{phi}{sub HL}=1/(2N). However, the method of phase detection suggested by those authors, obtaining the difference of the photocurrents at the output ports of the interferometer, is not sensitive to the phase difference between the two interferometer paths; in fact, the photocurrent vanishes. In this paper we show that the use of parity measurements on just one of the output modes not only is sensitive to the phase difference but that the sensitivity approaches the Heisenberg limit for large N.

  4. Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet.

    PubMed

    Fu, Mingxuan; Imai, Takashi; Han, Tian-Heng; Lee, Young S

    2015-11-06

    The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χ(kagome), deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χ(kagome) that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.

  5. 3 d -electron Heisenberg pyrochlore Mn2Sb2O7

    NASA Astrophysics Data System (ADS)

    Peets, Darren C.; Sim, Hasung; Avdeev, Maxim; Park, Je-Geun

    2016-11-01

    In frustrated magnetic systems, geometric constraints or the competition among interactions introduce extre-mely high degeneracy and prevent the system from readily selecting a low-temperature ground state. The most frustrated known spin arrangement is on the pyrochlore lattice, but nearly all magnetic pyrochlores have unquenched orbital angular momenta, constraining the spin directions through spin-orbit coupling. Pyrochlore Mn2Sb2O7 is an extremely rare Heisenberg pyrochlore system with directionally unconstrained spins and low chemical disorder. We show that it undergoes a spin-glass transition at 5.5 K, which is suppressed by disorder arising from Mn vacancies, indicating this ground state to be a direct consequence of the spins' interactions. The striking similarities to 3 d transition-metal pyrochlores with unquenched angular momenta suggests that the low spin-orbit coupling in the 3 d block makes Heisenberg pyrochlores far more accessible than previously imagined.

  6. Genome wide expression profiling of angiogenic signaling and the Heisenberg uncertainty principle.

    PubMed

    Huber, Peter E; Hauser, Kai; Abdollahi, Amir

    2004-11-01

    Genome wide DNA expression profiling coupled with antibody array experiments using endostatin to probe the angiogenic signaling network in human endothelial cells were performed. The results reveal constraints on the measuring process that are of a similar kind as those implied by the uncertainty principle of quantum mechanics as described by Werner Heisenberg. We describe this analogy and argue for its heuristic utility in the conceptualization of angiogenesis as an important step in tumor formation.

  7. Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

    NASA Astrophysics Data System (ADS)

    Mert, Gülistan

    2012-09-01

    The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.

  8. Phase transition in Heisenberg stacked triangular antiferromagnets: end of a controversy.

    PubMed

    Ngo, V Thanh; Diep, H T

    2008-09-01

    By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first order, contrary to results of earlier MC simulations using old-fashioned methods. Our result lends support to the conclusion of a nonperturbative renormalization group performed on an effective Hamiltonian. It puts an end to a 20-year -long controversial issue.

  9. Ordering of the three-dimensional Heisenberg spin glass in magnetic fields.

    PubMed

    Kawamura, H; Imagawa, D

    2001-11-12

    Spin and chirality orderings of the three-dimensional Heisenberg spin glass are studied under magnetic fields in light of the recently developed spin-chirality decoupling-recoupling scenario. It is found by Monte Carlo simulations that the chiral-glass transition and the chiral-glass ordered state, which are essentially of the same character as their zero-field counterparts, occur under magnetic fields. The implication to the experimental phase diagram is discussed.

  10. Probing of the interfacial Heisenberg and Dzyaloshinskii-Moriya exchange interaction by magnon spectroscopy

    NASA Astrophysics Data System (ADS)

    Zakeri, Khalil

    2017-01-01

    This Topical Review presents an overview of the recent experimental results on the quantitative determination of the magnetic exchange parameters in ultrathin magnetic films and multilayers grown on different substrates. The experimental approaches for probing both the symmetric Heisenberg and the antisymmetric Dzyaloshinskii-Moriya exchange interaction in ultrathin magnetic films and at interfaces are discussed in detail. It is explained how the experimental spectrum of magnetic excitations can be used to quantify the strength of these interactions.

  11. Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator

    PubMed Central

    Chang, Der-Chen; Li, Yutian

    2015-01-01

    The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries. PMID:25792966

  12. Anisotropic exchange-interaction model: From the Potts model to the exchange-interaction model

    NASA Astrophysics Data System (ADS)

    King, T. C.; Chen, H. H.

    1995-04-01

    A spin model called the anisotropic exchange-interaction model is proposed. The Potts model, the exchange-interaction model, and the spin-1/2 anisotropic Heisenberg model are special cases of the proposed model. Thermodynamic properties of the model on the bcc and the fcc lattices are determined by the constant-coupling approximation.

  13. Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

    NASA Astrophysics Data System (ADS)

    Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

    2015-03-01

    We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

  14. Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance

    NASA Astrophysics Data System (ADS)

    Dressel, Justin; Nori, Franco

    2014-02-01

    We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations relies on an implicit assumption that is generally incompatible with the Bell-Kochen-Specker-Spekkens contextuality theorems, and which results in averaging the deviations over a non-positive-semidefinite joint quasiprobability distribution. For unbiased measurements, the error admits a concrete interpretation as the dispersion in the estimation of the mean induced by the measurement ambiguity. We demonstrate how to directly measure not only this dispersion but also every observable moment with the same experimental data, and thus demonstrate that perfect distributional estimations can have nonzero error according to this measure. We conclude that the inequalities using these definitions do not capture the spirit of Heisenberg's eponymous inequality, but do indicate a qualitatively different relationship between dispersion and disturbance that is appropriate for ensembles being probed by all outcomes of an apparatus. To reconnect with the discussion of Heisenberg, we suggest alternative definitions of error and disturbance that are intrinsic to a single apparatus outcome. These definitions naturally involve the retrodictive and interdictive states for that outcome, and produce complementarity and error-disturbance inequalities that have the same form as the traditional Heisenberg relation.

  15. Born-Jordan Quantization and the Equivalence of the Schrödinger and Heisenberg Pictures.

    PubMed

    de Gosson, Maurice A

    The aim of the famous Born and Jordan 1925 paper was to put Heisenberg's matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg's theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger's wave mechanics cannot be equivalent to Heisenberg's more physically motivated matrix mechanics unless its observables are quantized using this rule, and not the more symmetric prescription proposed by Weyl in 1926, which has become the standard procedure in quantum mechanics. This observation confirms the superiority of Born-Jordan quantization, as already suggested by Kauffmann. We also show how to explicitly determine the Born-Jordan quantization of arbitrary classical variables, and discuss the conceptual advantages in using this quantization scheme. We finally suggest that it might be possible to determine the correct quantization scheme by using the results of weak measurement experiments.

  16. Non-linear spin wave theory results for the frustrated [Formula: see text] Heisenberg antiferromagnet on a body-centered cubic lattice.

    PubMed

    Majumdar, Kingshuk; Datta, Trinanjan

    2009-10-07

    At zero temperature the sublattice magnetization of the quantum spin- 1/2 Heisenberg antiferromagnet on a body-centered cubic lattice with competing first and second neighbor exchange (J(1) and J(2)) is investigated using the non-linear spin wave theory. The zero temperature phases of the model consist of a two sublattice Néel phase for small J(2) (AF(1)) and a collinear phase at large J(2) (AF(2)). We show that quartic corrections due to spin wave interactions enhance the sublattice magnetization in both the AF(1) and the AF(2) phase. The magnetization corrections are prominent near the classical transition point of the model and in the J(2)>J(1) regime. The ground state energy with quartic interactions is also calculated. It is found that up to quartic corrections the first order phase transition (previously observed in this model) between the AF(1) and the AF(2) phase survives.

  17. Topological Phases of Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2016-12-01

    A series of symmetry-protected topological (SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In case one of the next-nearest-neighbor interactions vanishes, the model reduces to the Δ-chain in which a series of spin-gap phases are found, as shown in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground-state phase boundaries are insensitive to the strength of the alternation in the next-nearest-neighbor interaction. These results are consistent with the analysis based on the nonlinear σ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.

  18. Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like-Decorated Square Lattice

    NASA Astrophysics Data System (ADS)

    Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki

    2017-01-01

    We study the ground-state phase diagram of a Heisenberg model with spin S = 1/2 on a diamond-like-decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the length of the diagonal bond to that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn 85, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of λc < λ < 2, are identical to the square-lattice dimer-covering states, which ignited renewed interest in high-dimensional diamond-like-decorated lattices. In order to determine the phase boundary λc, we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain λc = 0.974. Furthermore, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram.

  19. DMRG Study of the S >= 1 quantum Heisenberg Antiferromagnet on a Kagome-like lattice without loops

    NASA Astrophysics Data System (ADS)

    Lamberty, R. Zach; Changlani, Hitesh J.; Henley, Christopher L.

    2013-03-01

    The Kagome quantum Heisenberg antiferromagnet, for spin up to S = 1 and perhaps S = 3 / 2 , is a prime candidate to realize a quantum spin liquid or valence bond crystal state, but theoretical or computational studies for S > 1 / 2 are difficult and few. We consider instead the same interactions and S >= 1 on the Husimi Cactus, a graph of corner sharing triangles whose centers are vertices of a Bethe lattice, using a DMRG procedure tailored for tree graphs. Since both lattices are locally identical, properties of the Kagome antiferromagnet dominated by nearest-neighbor spin correlations should also be exhibited on the Cactus, whereas loop-dependent effects will be absent on the loopless Cactus. Our study focuses on the possible transition(s) that must occur with increasing S for the Cactus antiferromagnet. (It has a disordered valence bond state at S = 1 / 2 but a 3-sublattice coplanar ordered state in the large S limit). We also investigate the phase diagram of the S = 1 quantum XXZ model with on-site anisotropy, which we expect to have three-sublattice and valence-bond-crystal phases similar to the kagome case. This work is supported by the National Science Foundation through a Graduate Research Fellowship to R. Zach Lamberty, as well as grant DMR-

  20. Calculations of localized modes on surface and impurity layer embedded in a semi-infinite Heisenberg ferromagnet

    SciTech Connect

    Tamine, M. . E-mail: moktam@hotmail.com; Boumeddine, F.

    2006-10-15

    We investigate the magnetic excitations for the magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of an impurity layer embedded within a semi-infinite ferromagnet. A Heisenberg model is employed to investigate the possibility that localized modes can occur with an impurity layer implanted within a semi-infinite ferromagnet. No electronic effects are considered. The theoretical approach employs the matching procedure in the mean field approximation and determines the propagating and evanescent spin amplitude fields including the contribution due to an applied field. The results are used to calculate the energies of localized modes associated with the impurity layer and with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. It is shown that more localized modes can occur and the modification of the spin wave spectra can be signaled by the appearance of surface and impurity modes, besides the bulk excitations. Also, the bulk spin fluctuations field, the spin waves localized on the surface as well as on impurity layer depend are shown to depend on the nature of the exchange coupling between spin sites, the values of spin sites and the position of the impurity layer from the surface.

  1. The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity

    NASA Astrophysics Data System (ADS)

    Setare, M. R.; Adami, H.

    2017-01-01

    In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern-Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity (GMMG) and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. Also the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the black hole.

  2. Spin-ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet.

    PubMed

    Liu, Tao; Li, Wei; Su, Gang

    2016-09-01

    Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the sqrt[3]×sqrt[3] state (i.e., the state with 120^{∘} spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m_{s}=1/3,23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T^{2} behavior, and the susceptibility approaches a finite constant as T→0. Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between q=0 state (i.e., the state with 120^{∘} spin configuration within a unit cell containing three sites) and sqrt[3]×sqrt[3] state in a spin-3/2 kagome XXZ model at the critical point Δ_{c}=0.54. This study provides reliable and useful information for further explorations on high-spin kagome physics.

  3. Spin-ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Liu, Tao; Li, Wei; Su, Gang

    2016-09-01

    Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the √{3 }×√{3 } state (i.e., the state with 120° spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m /ms=1 /3 ,23 /27 , and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T2 behavior, and the susceptibility approaches a finite constant as T →0 . Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between q =0 state (i.e., the state with 120° spin configuration within a unit cell containing three sites) and √{3 }×√{3 } state in a spin-3/2 kagome XXZ model at the critical point Δc=0.54 . This study provides reliable and useful information for further explorations on high-spin kagome physics.

  4. Thermally driven classical Heisenberg chain with a spatially varying magnetic field: thermal rectification and negative differential thermal resistance

    NASA Astrophysics Data System (ADS)

    Bagchi, Debarshee

    2015-02-01

    Thermal rectification and negative differential thermal resistance are two important features that have direct technological relevance. Here, we study the classical one-dimensional Heisenberg model, driven thermally by heat baths attached at the two ends of the system and in the presence of an external magnetic field that varies monotonically in space. Heat conduction in this system is studied using a local energy conserving dynamics. It is found that by suitably tuning the spatially varying magnetic field, the structurally homogeneous symmetric system exhibits both thermal rectification and negative differential thermal resistance. Thermal rectification, in some parameter ranges, shows interesting dependencies on the average temperature T and the system size N—rectification improves as T and N are increased. Using the microscopic dynamics of the spins we present a physical picture to understand thermal rectification as exhibited by this system and provide supporting numerical evidence. Emergence of the negative response in this system can be controlled by tuning the external magnetic field alone, which can have possible applications in the fabrication of novel thermal devices.

  5. Enhanced magnetocaloric effect in the proximity of magnetization steps and jumps of spin-1/2 XXZ Heisenberg regular polyhedra

    NASA Astrophysics Data System (ADS)

    KarǏová, Katarína; Strečka, Jozef; Richter, Johannes

    2017-03-01

    The magnetization process and adiabatic demagnetization of antiferromagnetic spin-1/2 XXZ Heisenberg clusters in the shape of regular polyhedra (tetrahedron, octahedron, cube, icosahedron and dodecahedron) are examined using the exact diagonalization method. It is demonstrated that a quantum (xy) part of the XXZ exchange interaction is a primary cause for the presence of additional intermediate magnetization plateaux and steps, which are totally absent in the limiting Ising case. The only exception to this rule is the spin-1/2 XXZ Heisenberg tetrahedron, which shows just a quantitative shift of the level-crossing fields related to two magnetization steps. It is shown that spin-1/2 XXZ Heisenberg regular polyhedra exhibit an enhanced magnetocaloric effect in the proximity of magnetization steps and jumps, which are accompanied with a rapid drop (rise) of temperature just above (below) the level-crossing field when the magnetic field is removed adiabatically.

  6. Enhanced magnetocaloric effect in the proximity of magnetization steps and jumps of spin-1/2 XXZ Heisenberg regular polyhedra.

    PubMed

    KarǏová, Katarína; Strečka, Jozef; Richter, Johannes

    2017-03-29

    The magnetization process and adiabatic demagnetization of antiferromagnetic spin-1/2 XXZ Heisenberg clusters in the shape of regular polyhedra (tetrahedron, octahedron, cube, icosahedron and dodecahedron) are examined using the exact diagonalization method. It is demonstrated that a quantum (xy) part of the XXZ exchange interaction is a primary cause for the presence of additional intermediate magnetization plateaux and steps, which are totally absent in the limiting Ising case. The only exception to this rule is the spin-1/2 XXZ Heisenberg tetrahedron, which shows just a quantitative shift of the level-crossing fields related to two magnetization steps. It is shown that spin-1/2 XXZ Heisenberg regular polyhedra exhibit an enhanced magnetocaloric effect in the proximity of magnetization steps and jumps, which are accompanied with a rapid drop (rise) of temperature just above (below) the level-crossing field when the magnetic field is removed adiabatically.

  7. Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder

    NASA Astrophysics Data System (ADS)

    Shinaoka, Hiroshi; Tomita, Yusuke; Motome, Yukitoshi

    2014-10-01

    Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disorder. The effective model is analyzed by classical Monte Carlo simulations using an extended loop algorithm. First, we discuss the phase diagrams in detail by showing the comprehensive Monte Carlo data for thermodynamic and magnetic properties. We show that the spin-glass transition temperature Tf is largely enhanced by the spin-lattice coupling b in the weakly disordered regime. By considering the limit of strong spin-lattice coupling, this enhancement is ascribed to the suppression of thermal fluctuations in semidiscrete degenerate manifold formed in the presence of the spin-lattice coupling. We also find that, by increasing the strength of disorder Δ, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by b, being almost independent of Δ. This is due to the fact that the spin-glass transition is triggered by the spin collinearity developed by the nematic order. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in spin-lattice order in the weakly disordered regime, the concomitant transition remains robust with Tf almost independent of Δ. We find that the magnetic susceptibility shows hysteresis between the field-cooled and zero-field-cooled data below Tf, and that the nonlinear susceptibility shows a negative divergence at the transition. These features are common to conventional spin-glass systems. Meanwhile, we find that the specific heat exhibits a broad peak at Tf, and that the

  8. Improving the Quality of Heisenberg Back-Action of Qubit Measurements made with Parametric Amplifiers

    NASA Astrophysics Data System (ADS)

    Sliwa, Katrina

    The quantum back-action of the measurement apparatus arising from the Heisenberg uncertainty principle is both a fascinating phenomenon and a powerful way to apply operations on quantum systems. Unfortunately, there are other effects which may overwhelm the Heisenberg back-action. This thesis focuses on two effects arising in the dispersive measurement of superconducting qubits made with two ultra-low-noise parametric amplifiers, the Josephson bifurcation amplifier (JBA) and the Josephson parametric converter (JPC). The first effect is qubit dephasing due to excess photons in the cavity coming from rogue radiation emitted by the first amplifier stage toward the system under study. This problem arises primarily in measurements made with the JBA, where a strong resonant pump tone is traditionally used to provide the energy for amplification. Replacing the single strong pump tone with two detuned pump tones minimized this dephasing to the point where the Heisenberg back-action of measurements made with the JBA could be observed. The second effect is reduced measurement efficiency arising from losses between the qubit and the parametric amplifier. Most commonly used parametric amplifiers operate in reflection, requiring additional lossy, magnetic elements known as circulators both to separate input from output, and to protect the qubits from dephasing due to the amplified reflected signal. This work presents two alternative directional elements, the Josephson circulator, which is both theoretically loss-less and does not rely upon the strong magnetic fields needed for traditional circulators, and the Josephson directional amplifier which does not send any amplified signal back toward the qubit. Both of these elements achieve directionality by interfering multiple parametric processes inside a single JPC, allowing for in-situ switching between the two modes of operation. This brings valuable experimental flexibility, and also makes these devices strong candidates for

  9. Giant spin gap and magnon localization in the disordered Heisenberg antiferromagnet Sr2Ir1−xRuxO4

    DOE PAGES

    Cao, Yue; Liu, X.; Xu, Wenhu; ...

    2017-03-06

    Here, we study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1–xRuxO4. The maximum energy of the magnetic excitation remains robust up to x = 0.77, with a gap opening at low dopings and increasing to over 150 meV at x = 0.77. At these higher Ru concentrations, the dispersive magnetic excitations in Sr2IrO4 are rendered essentially momentum independent. Up to a Ru concentration of x = 0.77, both experiments and first-principles calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder.more » Under the coherent potential approximation, we reproduce the experimental magnetic excitations using the disordered Heisenberg antiferromagnetic model with suppressed next-nearest-neighbor ferromagnetic coupling.« less

  10. Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets Sr2CuO2Cl2 and Sr2Cu3O4Cl2.

    PubMed

    Kim, Y J; Birgeneau, R J; Chou, F C; Erwin, R W; Kastner, M A

    2001-04-02

    We report a neutron scattering study of the long-wavelength dynamic spin correlations in the model two-dimensional S = 1/2 square lattice Heisenberg antiferromagnets Sr2CuO2Cl2 and Sr2Cu3O4Cl2. The characteristic energy scale, omega(0)(T/J), is determined by measuring the quasielastic peak width in the paramagnetic phase over a wide range of temperature ( 0.2 less similarT/J less similar0.7). The obtained values for omega(0)(T/J) agree quantitatively between the two compounds and also with values deduced from quantum Monte Carlo simulations. The combined data show scaling behavior, omega approximately xi(-z), over the entire temperature range with z = 1.0(1), in agreement with dynamic scaling theory.

  11. Ba8CoNb6O24 : A spin-1/2 triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit

    NASA Astrophysics Data System (ADS)

    Rawl, R.; Ge, L.; Agrawal, H.; Kamiya, Y.; Dela Cruz, C. R.; Butch, N. P.; Sun, X. F.; Lee, M.; Choi, E. S.; Oitmaa, J.; Batista, C. D.; Mourigal, M.; Zhou, H. D.; Ma, J.

    2017-02-01

    The perovskite Ba8CoNb6O24 comprises equilateral effective spin-1/2 Co2 + triangular layers separated by six nonmagnetic layers. Susceptibility, specific heat, and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that Ba8CoNb6O24 is basically a two-dimensional magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, Ba8CoNb6O24 is very close to be a realization of the paradigmatic spin-1/2 triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperatures according to the Mermin and Wagner theorem.

  12. Magnetic structure of the S =1/2 quasi-two-dimensional square-lattice Heisenberg antiferromagnet Sr2CuTeO6

    NASA Astrophysics Data System (ADS)

    Koga, Tomoyuki; Kurita, Nobuyuki; Avdeev, Maxim; Danilkin, Sergey; Sato, Taku J.; Tanaka, Hidekazu

    2016-02-01

    The magnetic structure of the double perovskite compound Sr2CuTeO6 was determined from neutron powder diffraction data. This material is magnetically described as an S =1 /2 quasi-two-dimensional square-lattice Heisenberg model with antiferromagnetic nearest-neighbor and next-nearest-neighbor interactions. Sr2CuTeO6 undergoes a magnetic phase transition at TN≃29 K. The spin structure below TN is Néel antiferromagnetic on the square lattice, which means that the nearest-neighbor interaction (J1) is stronger than the next-nearest-neighbor interaction (J2), in contrast to other isostructural compounds such as Ba2CuWO6 and Sr2CuWO6 , for which | J1|<| J2| is realized.

  13. Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder

    NASA Astrophysics Data System (ADS)

    Schmidiger, D.; Povarov, K. Yu.; Galeski, S.; Reynolds, N.; Bewley, R.; Guidi, T.; Ollivier, J.; Zheludev, A.

    2016-06-01

    Properties of the depleted Heisenberg spin ladder material series (C7 H10 N )2Cu1 -zZnz Br4 have been studied by the combination of magnetic measurements and neutron spectroscopy. Disorder-induced degrees of freedom lead to a specific magnetic response, described in terms of emergent strongly interacting "spin island" objects. The structure and dynamics of the spin islands is studied by high-resolution inelastic neutron scattering. This allows us to determine their spatial shape and to observe their mutual interactions, manifested by strong spectral in-gap contributions.

  14. A class of simple weight modules over the twisted Heisenberg-Virasoro algebra

    NASA Astrophysics Data System (ADS)

    Chen, Haibo; Han, Jianzhi; Su, Yucai

    2016-10-01

    A class of weight modules M ( V , a ) over the twisted Heisenberg-Virasoro H are constructed, which includes modules of intermediate series, where V is an H ¯ r , d -module and a is a complex number. We give the necessary and sufficient conditions under which these modules are simple and also determine all the equivalent simple modules in this class. Moreover, we show that simple modules in this class are new. Finally, we construct a class of new simple non-weight H -modules.

  15. Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

    NASA Astrophysics Data System (ADS)

    Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong

    2010-07-01

    This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.

  16. Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems

    PubMed Central

    Ma, Xiao-song; Dakić, Borivoje; Kropatschek, Sebastian; Naylor, William; Chan, Yang-hao; Gong, Zhe-xuan; Duan, Lu-ming; Zeilinger, Anton; Walther, Philip

    2014-01-01

    Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology. PMID:24394808

  17. Heisenberg-Limited Qubit Read-Out with Two-Mode Squeezed Light

    NASA Astrophysics Data System (ADS)

    Didier, Nicolas; Kamal, Archana; Oliver, William D.; Blais, Alexandre; Clerk, Aashish A.

    2015-08-01

    We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, it is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics.

  18. Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass

    PubMed

    Hukushima; Kawamura

    2000-02-01

    Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.

  19. Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet.

    PubMed

    Sknepnek, Rastko; Vojta, Thomas; Vojta, Matthias

    2004-08-27

    We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.

  20. Spin-glass transition of the three-dimensional Heisenberg spin glass.

    PubMed

    Campos, I; Cotallo-Aban, M; Martin-Mayor, V; Perez-Gaviro, S; Tarancon, A

    2006-11-24

    It is shown, by means of Monte Carlo simulation and finite size scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass ordering develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes it possible to thermalize lattices of size L = 32, larger than in any previous spin-glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allows us to consider scaling corrections.

  1. High-energy magnon dispersion and multimagnon continuum in the two-dimensional Heisenberg antiferromagnet.

    PubMed

    Sandvik, A W; Singh, R R

    2001-01-15

    We use quantum Monte Carlo simulations and numerical analytic continuation to study high-energy spin excitations in the two-dimensional S = 1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse (x) and longitudinal (z) dynamic spin structure factors Sx,z(q,omega) at q = (pi,0) and (pi/2, pi/2). Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at (pi,0) is 10% lower than at (pi/2, pi/2). We also discuss the transverse and longitudinal multimagnon continua and their relevance to neutron scattering experiments.

  2. Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields.

    PubMed

    Imagawa, Daisuke; Kawamura, Hikaru

    2004-02-20

    The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.

  3. Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling.

    PubMed

    Mryglod, I M; Omelyan, I P; Folk, R

    2001-04-02

    The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.

  4. Quantum phase transition of the randomly diluted heisenberg antiferromagnet on a square lattice

    PubMed

    Kato; Todo; Harada; Kawashima; Miyashita; Takayama

    2000-05-01

    Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.

  5. Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems.

    PubMed

    Ma, Xiao-song; Dakić, Borivoje; Kropatschek, Sebastian; Naylor, William; Chan, Yang-hao; Gong, Zhe-xuan; Duan, Lu-ming; Zeilinger, Anton; Walther, Philip

    2014-01-07

    Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.

  6. Topological Hall effect in thin films of the Heisenberg ferromagnet EuO

    NASA Astrophysics Data System (ADS)

    Ohuchi, Y.; Kozuka, Y.; Uchida, M.; Ueno, K.; Tsukazaki, A.; Kawasaki, M.

    2015-06-01

    We report on the topological Hall effect (THE) in centrosymmetric EuO thin films. This THE signal persists down to the lowest temperature in the metallic region below 50 K for the films thinner than 200 nm. The signal rapidly disappears by tilting the applied magnetic field from surface normal, suggestive of noncoplanar spin configuration such as two-dimensional skyrmions. This observation possibly substantiates the theoretical proposal of magnetic skyrmions in 2D Heisenberg ferromagnets in marked contrast to better established B 20 -type chiral helimagnets.

  7. Ferroelectricity Driven by Dzyaloshinskii-Moriya Interaction in an Anisotropic Heisenberg Antiferromagnetic Chain

    NASA Astrophysics Data System (ADS)

    Qi, Yan; Du, An

    2012-06-01

    We have made a theoretical study on the ferroelectricity and ferromagnetism in an antiferromagnetic Heisenberg chain with a Dzyaloshinskii-Moriya interaction which may induce ferroelectricity in some low-dimensional magnetic materials. Based on the transfer-matrix method, we obtain the analytical results of the average magnetization, polarization and magnetic susceptibility. And these physical quantities as functions of temperature and applied field are discussed respectively under various conditions. We find that the temperature dependence of the magnetic susceptibility exhibits different responses for the external field applied along the chain and perpendicular to the chain, demonstrating the important role of anisotropy.

  8. The Hydrogen Atom: The Rutherford Model

    NASA Astrophysics Data System (ADS)

    Tilton, Homer Benjamin

    1996-06-01

    Early this century Ernest Rutherford established the nuclear model of the hydrogen atom, presently taught as representing the best visual model after modification by Niels Bohr and Arnold Sommerfeld. It replaced the so-called "plum pudding" model of J. J. Thomson which held sway previously. While the Rutherford model represented a large step forward in our understanding of the hydrogen atom, questions remained, and still do.

  9. A Pseudo-Quantum Triad: Schrödinger's Equation, the Uncertainty Principle, and the Heisenberg Group

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.

    2012-05-01

    We show that the paradigmatic quantum triad "Schrödinger equation-Uncertainty principle-Heisenberg group" emerges mathematically from classical mechanics. In the case of the Schrödinger equation, this is done by extending the metaplectic representation of linear Hamiltonian flows to arbitrary flows; for the Heisenberg group this follows from a careful analysis of the notion of phase of a Lagrangian manifold, and for the uncertainty principle it suffices to use tools from multivariate statistics together with the theory of John's minimum volume ellipsoid. Thus, the mathematical structure needed to make quantum mechanics emerge already exists in classical mechanics.

  10. High-resolution Monte Carlo study of the multicritical point in the three-dimensional XXZ Heisenberg antiferromagnet.

    PubMed

    Hu, Siyan; Tsai, Shan-Ho; Landau, D P

    2014-03-01

    We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

  11. High-resolution Monte Carlo study of the multicritical point in the three-dimensional XXZ Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Hu, Siyan; Tsai, Shan-Ho; Landau, D. P.

    2014-03-01

    We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

  12. Chern-Simons theory of the anisotropic quantum Heisenberg antiferromagnet on a square lattice

    NASA Astrophysics Data System (ADS)

    Lopez, Ana; Rojo, A. G.; Fradkin, Eduardo

    1994-06-01

    We consider the anisotropic quantum Heisenberg antiferromagnetic (with anistropy λ) on a square lattice using a Chern-Simons (or Wigner-Jordan) approach. We show that the average field approximation (AFA) yields a phase diagram with two phases: a Neèl state for λ>λc and a flux phase for λ<λc separated by a second-order transition at λc<1. We show that this phase diagram does not describe the XY regime of the antiferromagnet. Fluctuations around the AFA induce relevant operators which yield the correct phase diagram. We find an equivalence between the antiferromagnet and a relativistic field theory of two self-interacting Dirac fermions coupled to a Chern-Simons gauge field. The field theory has a phase diagram with the correct number of Goldstone modes in each regime and a phase transition at a critical coupling λ*>λc. We identify this transition with the isotropic Heisenberg point. It has a nonvanishing Neèl order parameter, which drops to zero discontinuously for λ<λ*.

  13. Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet

    SciTech Connect

    Fu, Mingxuan; Imai, Takahashi; Han, Tian -Heng; Lee, Young S.

    2015-11-06

    Here, the kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χkagome, deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χkagome that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.

  14. Characterization of Phase Transition in Heisenberg Fluids from Density Functional Theory

    NASA Astrophysics Data System (ADS)

    Li, Liang-Sheng; Li, Li; Chen, Xiao-Song

    2009-02-01

    The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation (MF). The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density ρ* = ρσ3 = 0.224 and the reduced temperature T* = kT/in = 1.87 (σ is the diameter of Heisenberg hard sphere and in is the coupling constant).

  15. Exact diagonalization of Heisenberg SU (N ) chains in the fully symmetric and antisymmetric representations

    NASA Astrophysics Data System (ADS)

    Nataf, Pierre; Mila, Frédéric

    2016-04-01

    Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg SU (N ) Hamiltonian with several particles per site living in a fully symmetric or antisymmetric representation of SU (N ) . The method, based on the use of standard Young tableaux, takes advantage of the full SU (N ) symmetry, allowing one to work directly in each irreducible representation of the global SU (N ) group. Since the SU (N ) singlet sector is often much smaller than the full Hilbert space, this enables one to reach much larger system sizes than with conventional exact diagonalizations. The method is applied to the study of Heisenberg chains in the symmetric representation with two and three particles per site up to N =10 and up to 20 sites. For the length scales accessible to this approach, all systems except the Haldane chain [SU (2 ) with two particles per site] appear to be gapless, and the central charge and scaling dimensions extracted from the results are consistent with a critical behavior in the SU (N ) level k Wess-Zumino-Witten universality class, where k is the number of particles per site. These results point to the existence of a crossover between this universality class and the asymptotic low-energy behavior with a gapped spectrum or a critical behavior in the SU (N ) level 1 WZW universality class.

  16. Conditions for the appearance of boundary modes in topological phases of Heisenberg spin ladders

    NASA Astrophysics Data System (ADS)

    Robinson, Neil; Atland, Alexander; Egger, Reinhold; Gergs, Nkilas; Konik, Robert; Li, Wei; Schuricht, Dirk; Tsvelik, Alexei; Weichselbaum, Andreas

    We consider the problem of delineating the necessary conditions for the appearance of boundary modes in extended SU (2) Heisenberg spin ladders. Specifically, we study Heisenberg ladders with rung exchange, J⊥, and ring exchange, JX, that admit a field theoretic description in terms of Majorana fermions in the continuum limit. In this description there are four Majorana fermions, arranged in a triplet and a singlet. This suggests there are four distinct phases, corresponding to the configurations of the signs of the triplet mt and singlet ms masses. We label these phases as: Haldane (mt > 0 ,ms < 0), rung singlet (mt < 0 ,ms > 0), VBS+ (mt ,ms > 0) and VBS- (mt ,ms < 0). Topologically, we find two of these phases support gapless boundary modes: the Haldane phase (the triplet forms a spin- 1 / 2 degree of freedom at the ends of the ladder) and the VBS+ phase, where all the Majorana fermions have gapless boundary modes. The absence of a gapless boundary mode in the rung singlet phase is surprising; we find that the singlet mode can become gapless if open boundary conditions are replaced with a continuous change in lattice parameters. We suggest a symmetry-allowed modification to the low-energy effective theory which may be responsible for this behavior.

  17. Field-Induced Multiple Reentrant Quantum Phase Transitions in Randomly Dimerized Antiferromagnetic S=1/2 Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2006-07-01

    The multiple reentrant quantum phase transitions in the S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with interchain mean field approximation. It is assumed that odd numbered bonds are antiferromagnetic with strength J and even numbered bonds can take the values JS and JW (JS > J > JW > 0) randomly with the probabilities p and 1- p, respectively. The pure version ( p=0 and 1) of this model has a spin gap but exhibits a field-induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0 < p < 1, antiferromagnetism is induced by randomness at the small field region where the ground state is disordered due to the spin gap in the pure version. At the same time, this model exhibits randomness-induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between transverse antiferromagnetic phases and disordered plateau phases with the increase of magnetic field for a moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and jumps between them. It is also found that antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low-lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.

  18. Coordinate Bethe ansatz computation for low temperature behavior of a triangular lattice of a spin-1 Heisenberg antiferromagnet

    SciTech Connect

    Shuaibu, A.; Rahman, M. M.

    2014-03-05

    We study the low temperature behavior of a triangular lattice quantum spin-1 Heisenberg antiferromagnet with single-site anisotropy by using coordinate Bethe ansatz method. We compute the standard two-particle Hermitian Hamiltonian, and obtain the eigenfunctions and eigenvalue of the system. The obtained results show a number of advantages in comparison with many results.

  19. Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}: A new telluro-phosphate with S=1/2 Heisenberg chain

    SciTech Connect

    Xia, Mingjun; Shen, Shipeng; Lu, Jun; Sun, Young; Li, R.K.

    2015-10-15

    A new telluro-phosphate compound Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, one dimensional [CuTePO{sub 7}]{sup 3−} chains are formed by tetrahedral PO{sub 4} and trigonal bi-pyramidal TeO{sub 4} joining square planar CuO{sub 4} groups. Those [CuTePO{sub 7}]{sup 3−} chains are inter-connected by sharing one oxygen atom from the TeO{sub 4} group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system. - Graphical abstract: Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, containing (CuTePO{sub 7}){sup 3−} chains formed by PO{sub 4} and TeO{sub 4} joining CuO{sub 4} groups, shows typical 1D Heisenberg antiferromagnetic chain model behavior as confirmed by magnetic measurements. - Highlights: • New telluro-phosphate Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} has been grown. • It features layered structure composed of [CuTePO{sub 7}]{sup 3−} chains and TeO{sub 4} groups. • It shows the Heisenberg antiferromagnetic chain behavior. • It is transparent in the range of 1000–2500 nm with a UV absorption edge of 393 nm.

  20. Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions

    NASA Astrophysics Data System (ADS)

    Djoufack, Z. I.; Tala-Tebue, E.; Nguenang, J. P.; Kenfack-Jiotsa, A.

    2016-10-01

    We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

  1. Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

    PubMed

    Djoufack, Z I; Tala-Tebue, E; Nguenang, J P; Kenfack-Jiotsa, A

    2016-10-01

    We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

  2. Bosonic and k-fermionic coherent states for a class of polynomial Weyl-Heisenberg algebras

    NASA Astrophysics Data System (ADS)

    Daoud, M.; Kibler, M. R.

    2012-06-01

    The aim of this paper is to construct coherent states à la Perelomov and à la Barut-Girardello for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, denoted by { A}_{ \\lbrace \\kappa \\rbrace }, depends on r real parameters and is an extension of the { A}_{ \\kappa } one-parameter algebra (Daoud and Kibler 2010 J. Phys. A: Math. Theor. 43 115303) which covers the cases of the su(1, 1) algebra (for κ > 0), the su(2) algebra (for κ < 0) and the h4 ordinary Weyl-Heisenberg algebra (for κ = 0). For finite-dimensional representations of { A}_{ \\lbrace \\kappa \\rbrace } and { A}_{ \\lbrace \\kappa \\rbrace , s }, where { A}_{ \\lbrace \\kappa \\rbrace , s } is a truncation of order s of { A}_{ \\lbrace \\kappa \\rbrace } in the sense of Pegg-Barnett, a connection is established with k-fermionic algebras (or quon algebras). This connection makes it possible to use generalized Grassmann variables for constructing certain coherent states. Coherent states of the Perelomov type are derived for infinite-dimensional representations of { A}_{ \\lbrace \\kappa \\rbrace } and for finite-dimensional representations of { A}_{ \\lbrace \\kappa \\rbrace } and { A}_{ \\lbrace \\kappa \\rbrace , s} through a Fock-Bargmann analytical approach based on the use of complex (or bosonic) variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in the case of infinite-dimensional representations of { A}_{ \\lbrace \\kappa \\rbrace }. In contrast, the construction of coherent states à la Barut-Girardello for finite-dimensional representations of { A}_{ \\lbrace \\kappa \\rbrace } and { A}_{ \\lbrace \\kappa \\rbrace , s } can be achieved solely at the price of replacing complex variables by generalized Grassmann (or k-fermionic) variables. Some of the results are applied to su(2), su(1, 1) and the harmonic oscillator (in a truncated or not truncated form). This article is part of a special issue of Journal of

  3. GENERAL: Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

    NASA Astrophysics Data System (ADS)

    Shan, Chuan-Jia; Cheng, Wei-Wen; Liu, Tang-Kun; Liu, Ji-Bing; Wei, Hua

    2008-09-01

    Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.

  4. Thermal rectification and negative differential thermal resistance in a driven two segment classical Heisenberg chain

    NASA Astrophysics Data System (ADS)

    Bagchi, Debarshee

    2013-12-01

    Using computer simulation we investigate thermal transport in a two segment classical Heisenberg spin chain with nearest neighbor interaction and in the presence of an external magnetic field. The system is thermally driven by heat baths attached at the two ends and transport properties are studied using energy conserving dynamics. We demonstrate that by properly tuning the parameters thermal rectification can be achieved—the system behaves as a good conductor of heat along one direction but becomes a bad conductor when the thermal gradient is reversed, and crucially depends on nonlinearity and spatial asymmetry. Moreover, suitable tuning of the system parameters gives rise to the counterintuitive and technologically important feature known as negative differential thermal resistance (NDTR). We find that the crucial factor responsible for the emergence of NDTR is a suitable mechanism for impeding the current in the bulk of the system.

  5. Ferrimagnetic and Long Period Antiferromagnetic Phases in High Spin Heisenberg Chains with D-Modulation

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2007-02-01

    The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method. It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains. On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy. Eventually, the magnetization is locked to fractional values of the saturated magnetization. These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition. The local spin profile is calculated to reveal the physical nature of each state. In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.

  6. Ground-State Phase Diagram of S = 2 Heisenberg Chains with Alternating Single-Site Anisotropy

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2014-03-01

    The ground-state phase diagram of S = 2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-D, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.

  7. Werner states and the two-spinors Heisenberg anti-ferromagnet

    NASA Astrophysics Data System (ADS)

    Batle, J.; Casas, M.; Plastino, A.; Plastino, A. R.

    2005-08-01

    We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. 87 (2001) 017901] and using the statistical tool called entropic non-triviality [P.W. Lamberti, M.T. Martin, A. Plastino, O.A. Rosso, Physica A 334 (2004) 119], that there is a one-to-one correspondence between (i) the mixing coefficient x of a Werner state, on the one hand, and (ii) the temperature T of the one-dimensional Heisenberg two-spin chain with a magnetic field B along the z-axis, on the other one. This is true for each value of B below a certain critical value B. The pertinent mapping depends on the particular B-value one selects within such a range.

  8. Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances

    NASA Astrophysics Data System (ADS)

    Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng

    2016-04-01

    Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

  9. Heisenberg symmetry and collective modes of one dimensional unitary correlated fermions

    NASA Astrophysics Data System (ADS)

    Abhinav, Kumar; Chandrasekhar, B.; Vyas, Vivek M.; Panigrahi, Prasanta K.

    2017-02-01

    The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an SO (2 , 1) symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency ω are predicted in one dimension, in contrast to the breathing modes with frequency 2ω in two dimensions.

  10. Magnon specific heat and free energy of Heisenberg ferromagnetic single-walled nanotubes: Green's function approach

    NASA Astrophysics Data System (ADS)

    Mi, Bin-Zhou; Zhai, Liang-Jun; Hua, Ling-Ling

    2016-01-01

    The effect of magnetic spin correlation on the thermodynamic properties of Heisenberg ferromagnetic single-walled nanotubes are comprehensively investigated by use of the double-time Green's function method. The influence of temperature, spin quantum number, diameter of the tube, anisotropy strength and external magnetic field to internal energy, free energy, and magnon specific heat are carefully calculated. Compared to the mean field approximation, the consideration of the magnetic correlation effect significantly improves the internal energy values at finite temperature, while it does not so near zero temperature, and this effect is related to the diameter of the tube, anisotropy strength, and spin quantum number. The magnetic correlation effect lowers the internal energy at finite temperature. As a natural consequence of the reduction of the internal energy, the specific heat is reduced, and the free energy is elevated.

  11. A note for Riesz transforms associated with Schrödinger operators on the Heisenberg Group

    NASA Astrophysics Data System (ADS)

    Liu, Yu; Tang, Guobin

    2017-03-01

    Let H^n be the Heisenberg group and Q=2n+2 be its homogeneous dimension. The Schrödinger operator is denoted by - Δ_{H}^n} + V, where Δ_{H^n} is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class {B_{{q_1}}} for {q_1} ≥Q/2. Let H^p_L(H^n) be the Hardy space associated with the Schrödinger operator for Q/Q+δ _0

  12. On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality

    PubMed Central

    Putz, Mihai V.

    2010-01-01

    Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function. PMID:21152325

  13. Exchange anisotropy and the dynamic phase transition in thin ferromagnetic Heisenberg films.

    PubMed

    Jang, Hyunbum; Grimson, Malcolm J; Hall, Carol K

    2003-10-01

    Monte Carlo simulations have been performed to investigate the dependence of the dynamic phase behavior on the bilinear exchange anisotropy of a classical Heisenberg spin system. The system under consideration is a planar thin ferromagnetic film with competing surface fields subject to a pulsed oscillatory external field. The results show that the films exhibit a single discontinuous dynamic phase transition (DPT) as a function of the anisotropy of the bilinear exchange interaction in the Hamiltonian. Furthermore, there is no evidence of stochastic resonance associated with the DPT. These results are in marked contrast to the continuous DPT observed in the same system as a function of temperature and applied field strength for a fixed bilinear exchange anisotropy.

  14. Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice

    NASA Astrophysics Data System (ADS)

    Choi, Seongsoo; Kim, Woohyun; Kim, Jongho

    2016-09-01

    We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits ) of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: N/spins!M ! (N spins-M ) ! >Norbits ) of the spin-1/2 Heisenberg antiferromagnet on the L ×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.

  15. The Néel temperature of a D-dimensional bcc Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Radošević, Slobodan M.; Rutonjski, Milica S.; Pantić, Milan R.; Pavkov-Hrvojević, Milica V.; Kapor, Darko V.; Škrinjar, Mario G.

    2011-12-01

    The double-time temperature-dependent Green's function method is used to determine the Néel temperature of a Heisenberg antiferromagnet with easy axis XXZ anisotropy on a D-dimensional bcc lattice. Exact equations within the random phase approximation (RPA) and Callen approximation (CA) in terms of generalized hypergeometric functions valid for arbitrary D, S, and η≥1 are given. Analytical and numerical results presented here strongly suggest that, for D≥2, the CA gives a higher critical temperature. It is also shown that the RPA set of self-consistent equations yields a Néel temperature closer to the experimental value for compound (CH 3NH 3) 2MnCl 4.

  16. Anomalous curie response of impurities in quantum-critical spin-1/2 Heisenberg antiferromagnets.

    PubMed

    Höglund, Kaj H; Sandvik, Anders W

    2007-07-13

    We consider a magnetic impurity in two different S=1/2 Heisenberg bilayer antiferromagnets at their respective critical interlayer couplings separating Néel and disordered ground states. We calculate the impurity susceptibility using a quantum Monte Carlo method. With intralayer couplings in only one of the layers (Kondo lattice), we observe an anomalous Curie constant C*, as predicted on the basis of field-theoretical work [S. Sachdev, Science 286, 2479 (1999)10.1126/science.286.5449.2479]. The value C* = 0.262 +/- 0.002 is larger than the normal Curie constant C=S(S+1)/3. Our low-temperature results for a symmetric bilayer are consistent with a universal C*.

  17. Multiple dynamic transitions in an anisotropic Heisenberg ferromagnet driven by polarized magnetic field.

    PubMed

    Acharyya, Muktish

    2004-02-01

    A uniaxially (along the Z axis) anisotropic Heisenberg ferromagnet, in the presence of time-dependent (but uniform over space) magnetic field, is studied by Monte Carlo simulation. The time-dependent magnetic field was taken as elliptically polarized where the resultant field vector rotates in the X-Z plane. The system is cooled (in the presence of the elliptically polarized magnetic field) from high temperature. As the temperature decreases, it was found that in the low anisotropy limit the system undergoes three successive dynamical phase transitions. These three dynamic transitions were confirmed by studying the temperature variation of dynamic "specific heat." The temperature variation of dynamic specific heat shows three peaks indicating three dynamic transition points.

  18. Anisotropic Heisenberg form of RKKY interaction in the one-dimensional spin-polarized electron gas

    NASA Astrophysics Data System (ADS)

    Valizadeh, M. M.

    2016-09-01

    We study the indirect exchange interaction between two localized magnetic moments, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, in a one-dimensional (1D) spin-polarized electron gas. We find explicit expressions for each term of this interaction, study their oscillatory behaviors as a function of the distance between two magnetic moments, R, and compare them with the known results for RKKY interaction in the case of 1D standard electron gas. We show this interaction can be written in an anisotropic Heisenberg form, E(R) = λ2χ xx(S1xS2x + S1yS2y) + λ2χ zzS1zS2z, coming from broken time-reversal symmetry of the host material.

  19. Strong equivalence principle in polymer quantum mechanics and deformed Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Kajuri, Nirmalya

    2016-10-01

    The strong equivalence principle (SEP) states that the description of a physical system in a gravitational field is indistinguishable from the description of the same system at rest in an accelerating frame. While this statement holds true in both general relativity and ordinary quantum mechanics, one expects it to fail when quantum gravity corrections are taken into account. In this paper we investigate the possible failure of the SEP in two quantum gravity inspired modifications of quantum mechanics—polymer quantum mechanics and deformed Heisenberg algebra. We find that the SEP fails to hold in both these theories. We estimate the deviation from SEP and find in both cases that it is too small to be measured in present day experiments.

  20. Collective dynamics in the Heisenberg pyrochlore antiferromagnet Gd2Sn2O7

    NASA Astrophysics Data System (ADS)

    Stewart, J. R.; Gardner, J. S.; Qiu, Y.; Ehlers, G.

    2008-10-01

    Gd2Sn2O7 is believed to be a good approximation to a Heisenberg antiferromagnet on a pyrochlore lattice with exchange and dipole-dipole interactions. The system is known to enter a long-range ordered ground state (the “Palmer Chalker” state) below Tc=1K with kord=(000) . However, persistent electronic spin fluctuations have been observed as T→0 . Using inelastic neutron scattering, we have studied the buildup of short-range spin-spin correlations as the temperature is lowered, and the eventual formation of a gapped long-range ordered state that is able to sustain spin waves below Tc . As a magnetic field is applied, new magnetic phases develop and the gap widens. These measurements show that Gd2Sn2O7 completely relieves itself of frustration, but the self-selected ground state is very delicate.

  1. Cat-states in the framework of Wigner-Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Dehghani, A.; Mojaveri, B.; Shirin, S.; Saedi, M.

    2015-11-01

    A one-parameter generalized Wigner-Heisenberg algebra (WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule [ x ˆ ,pˆλ ] = i(1 + 2 λ R ˆ) and also highlights the dynamical symmetries of the pseudo-harmonic oscillator (PHO). The present article is devoted to the study of new cat-states built from λ-deformed Schrödinger coherent states, which according to the Barut-Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel's parameter and quadrature squeezing with respect to the λ-deformed canonical pairs (x ˆ ,pˆλ) . It is shown that these states minimize the uncertainty relations of each pair of the su(1 , 1) components.

  2. Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: Exact results

    NASA Astrophysics Data System (ADS)

    Popkov, V.; Karevski, D.; Schütz, G. M.

    2013-12-01

    We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle θ. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady-state currents scale as 1/N2 for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2θ/N.

  3. Quantum Critical Scaling and Temperature-Dependent Logarithmic Corrections in the Spin-Half Heisenberg Chain

    SciTech Connect

    Starykh, O.; Singh, R.; Sandvik, A.

    1997-01-01

    Low temperature dynamics of the S=(1)/(2) Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form expressions for the dynamic susceptibility and the NMR relaxation rates 1/T{sub 1} and 1/T{sub 2G} are obtained, and are argued to improve the agreement with recent experiments. Scaling in q/T and {omega}/T are violated due to these logarithmic terms. Numerical results show that the logarithmic corrections are very robust. While not yet in the asymptotic low temperature regime, they provide striking qualitative confirmation of the theoretical results. {copyright} {ital 1997} {ital The American Physical Society}

  4. Modified Spin-Wave Theory on Low-Dimensional Heisenberg Ferrimagnets: A New Robust Formulation

    NASA Astrophysics Data System (ADS)

    Noriki, Yusaku; Yamamoto, Shoji

    2017-03-01

    We propose a new scheme for modifying conventional spin waves so as to precisely describe low-dimensional Heisenberg ferrimagnets at finite temperatures. What is called the modified spin-wave theory was initiated by Takahashi, who intended to calculate the low-temperature thermodynamics of low-dimensional Heisenberg ferromagnets, where Holstein-Primakoff bosons are constrained to keep the total uniform magnetization zero in a straightforward manner. If the concept of an ideal Bose gas with a fixed density is applied to antiferromagnets and ferrimagnets, the formulation is no longer trivial, having rich variety in the way how the conventional spin waves, especially those in ferrimagnets, are constrained and brought into interaction. Which magnetization should be kept zero, uniform, staggered, or both? One or more chemical potentials can be introduced so as to satisfy the relevant constraint condition either in diagonalizing the Hamiltonian or in minimizing the free energy, making the Bogoliubov transformation dependent on temperature or leaving it free from temperature dependence. We can bring the thus-modified spin waves into interaction on the basis of the Hartree-Fock approximation or through the use of Wick's theorem in an attempt to refine their descriptions. Comparing various modification schemes both numerically and analytically in one and two dimensions, we eventually find an excellent bosonic language capable of describing heterogeneous quantum magnets on a variety of lattices over the whole temperature range — Wick's-theorem-based interacting spin waves modified so as to keep every sublattice magnetization zero via the temperature-dependent Bogoliubov transformation.

  5. A Test of Convection Models for IMF Bz North

    DTIC Science & Technology

    1990-01-01

    NOTATION *Utah State University , Logan, Utah 84322 **Goddard Space Flight Center, Greenbelt, MD 20771 - Reprinted from Planet Space Sci., Vol. 38, No. 9 pp...the Utah State University Ionospheric Model can provide insight as to which convection model applies to given situations. The model was run to obtain...MAYNARD Geophysics Laboratory, Hanscom AFB, MA 01731, U.S.A. J. J. SOJKA and R. W. SCHUNK Utah State University , Logan, Utah 84;22, U.S.A. and J. P

  6. Generation of maximally entangled states of a Bose-Einstein condensate and Heisenberg-limited phase resolution

    SciTech Connect

    Gerry, Christopher C.; Campos, R. A.

    2003-08-01

    We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.

  7. Characterization of Topological Phases of Spin-1/2 Frustrated Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chains by Entanglement Spectrum

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo

    2016-02-01

    The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.

  8. Heisenberg Probably Slept Here: The Lives, Times, and Ideas of the Great Physicists of the 20th Century

    NASA Astrophysics Data System (ADS)

    Brennan, Richard P.

    1998-09-01

    "Here is a book I wish I had when taking physics my senior year in high school!" -Book Report A lively illumination of modern physics' marquee players, featuring: * Albert Einstein * Max Planck * Ernest Rutherford * Niels Bohr * Werner Heisenberg * Richard Feynman * Murray Gell-Mann "Brennan has a knack for explaining difficult technicalities simply. His essays give a useful summary of twentieth-century science." -Financial Times "Highly recommended to expert and layperson alike." -Choice

  9. Boundary-induced spin-density waves in linear Heisenberg antiferromagnetic spin chains with S ≥1

    NASA Astrophysics Data System (ADS)

    Dey, Dayasindhu; Kumar, Manoranjan; Soos, Zoltán G.

    2016-10-01

    Linear Heisenberg antiferromagnets (HAFs) are chains of spin-S sites with isotropic exchange J between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin SG when S ≥1 . The ground state of open chains of N spins has SG=0 or S , respectively, for even or odd N . Density-matrix renormalization-group calculations with different algorithms for even and odd N are presented up to N =500 for the energy and spin densities ρ (r ,N ) of edge states in HAFs with S =1 , 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with ρ (r ,N ) ∝(-1) r -1 for r =1 ,2 ,...,N . The SDWs are in phase when N is odd, are out of phase when N is even, and have finite excitation energy Γ (N ) that decreases exponentially with N for integer S and faster than 1 /N for half integer S . The spin densities and excitation energy are quantitatively modeled for integer S chains longer than 5 ξ spins by two parameters, the correlation length ξ and the SDW amplitude, with ξ =6.048 for S =1 and 49.0 for S =2 . The BI-SDWs of S =3 /2 chains are not localized and are qualitatively different for even and odd N . Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases |Γ (N )| and weakens the size dependence. The nonlinear sigma model (NL σ M ) has been applied to the HAFs, primarily to S =1 with even N , to discuss spin densities and exchange between localized states at the ends as Γ (N ) ∝(-1) Nexp(-N /ξ ) . S =1 chains with odd N are fully consistent with the NL σ M ; S =2 chains have two gaps Γ (N ) with the same ξ as predicted whose ratio is 3.45 rather than 3; the NL σ M is more approximate for S =3 /2 chains with even N and is modified for exchange between ends for odd N .

  10. Randomness-Induced Quantum Spin Liquid Behavior in the s = 1/2 Random J1-J2 Heisenberg Antiferromagnet on the Honeycomb Lattice

    NASA Astrophysics Data System (ADS)

    Uematsu, Kazuki; Kawamura, Hikaru

    2017-04-01

    We investigate the ground-state and finite-temperature properties of the bond-random s = 1/2 Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, J1 and J2, by the exact diagonalization and the Hams-de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (J2/J1) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba3CuSb2O9 and 6HB-Ba3NiSb2O9 exhibiting the gapless QSL-like behaviors are discussed.

  11. Reducing Lag in Virtual Displays Using Multiple Model Adaptive Estimation

    DTIC Science & Technology

    1995-12-01

    time varying behavior. Kleinman [4] proposed an optimal control model for human performance in a closed loop. This model interprets human perception as a...Washington, D. C: NASA, 1963. 3. Arthur , Kevin W., Kellogg, S. Booth, Colin Ware, Evaluating 3D Task Performance for Fish Tank Virtual Worlds," ACM...of Describing Behavior," Human Factors, volume 19, number 4,1977. 13. Kozak, J. J., P. A. Hancock, E. J. Arthur , S. T. Chrysler, "Transfer of Training

  12. The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains.

    PubMed

    Fertitta, Edoardo; El Khatib, Muammar; Bendazzoli, Gian Luigi; Paulus, Beate; Evangelisti, Stefano; Leininger, Thierry

    2015-12-28

    The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.

  13. Dynamic Critical Behavior of The Anisotropic Classical Heisenberg Antiferromagnet in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Bunker, Alex; Landau, D. P.; Chen, Kun

    1996-03-01

    Using Monte Carlo and spin-dynamics techniques^1 we studied the dynamic behavior of the body-centered cubic classical Heisenberg antiferromagnet with single site anisotropy. In order that we may directly compare our results to experiment we have set the single site anisotropy term to match the degree of anisotropy found^2 in MnF_2. Through the determination and analysis of the form of the neutron scattering function S(q,ω) at and below T_c, we have found the dispersion curves for different temperatures and studied the critical dynamics. We have compared our results to simulations^1 for the isotropic case and experiment^2 on MnF_2. Research supported in part by the NSF ^**current address: Solid State Division, Oak Ridge National Laboratory ^1 K. Chen, D. P. Landau, Phys. Rev. B \\underline49, 3266, (1994) ^2 J. Als-Nielsen in Phase Transitions and Critical Phenomena, ed. C. Domb, M. S. Green, (Academic Press, 1976)

  14. Critical Dynamics of The Classical 3-D Heisenberg Antiferromagnet with Anisotropy

    NASA Astrophysics Data System (ADS)

    Bunker, Alex; Chen, Kun; Landau, D. P.

    1997-03-01

    Using large scale Monte Carlo and spin-dynamics techniques^1 we studied the dynamic behavior of the body-centered cubic classical Heisenberg antiferromagnet with single site anisotropy. In order to directly compare our results to experiment, we set the anisotropy to match that found^2 in FeF2 (strong anisotropy) and MnF2 (weak anisotropy). We determined the form of the dynamic structure factor, S(q,ω), at Tc and found agreement with experiment^3 and theory^4 which indicate a strong diffusive longitudinal component that is critical and a weak, non-critical propagative transverse component. Supported in part by the NSF ^**current address: Solid State Division, ORNL ^1 K. Chen, D. P. Landau, Phys. Rev. B \\underline49, 3266, (1994) ^2 J. Als-Nielsen in Phase Transitions and Critical Phenomena, \\underline5A, C. Domb, M. S. Green, (Academic Press, 1976) ^3 M. P. Schulhof et. al., Phys. Rev. B \\underline1, 2304, (1970) ^4 S. W. Lovesey, E. Balcar, J. Phys. Cond. Matt. \\underline7, 2147, (1995)

  15. Electronic properties of corrugated graphene: the Heisenberg principle and wormhole geometry in the solid state.

    PubMed

    Atanasov, Victor; Saxena, Avadh

    2011-05-04

    Adopting a purely two-dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting the off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts, and in the process the embedding of this surface into the three-dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or 'straintronics' is clearly an important field of study in graphene. This opens an avenue to producing electronic devices: micro- and nano-electromechanical systems (MEMS and NEMS), where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks in the curved space-time of general relativity. In this context we explore a two-dimensional cross-section of the wormhole geometry, realized with graphene as a solid state thought experiment.

  16. Collective Dynamics in the Heisenberg Pyrochlore Antiferromagnet Gd2Sn2O7

    SciTech Connect

    Ehlers, Georg

    2008-01-01

    Gd{sub 2}Sn{sub 2}O{sub 7} is believed to be a good approximation to a Heisenberg antiferromagnet on a pyrochlore lattice with exchange and dipole-dipole interactions. The system is known to enter a long-range ordered ground state (the 'Palmer Chalker' state) below T{sub c} = 1 K with k{sub ord} = (000). However, persistent electronic spin fluctuations have been observed as T {yields} 0. Using inelastic neutron scattering, we have studied the buildup of short-range spin-spin correlations as the temperature is lowered, and the eventual formation of a gapped long-range ordered state that is able to sustain spin waves below T{sub c}. As a magnetic field is applied, new magnetic phases develop and the gap widens. These measurements show that Gd{sub 2}Sn{sub 2}O{sub 7} completely relieves itself of frustration, but the self-selected ground state is very delicate.

  17. Anomalous Curie response of an impurity in a quantum critical spin-1/2 Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Höglund, Kaj; Sandvik, Anders

    2007-03-01

    There is a disagreement concerning the low-temperature (T) magnetic susceptibility χ^zimp˜C/T of a spin-S impurity in a nearly quantum critical antiferromagnetic host. Field-theoretical work [1] predicted an anomalous Curie constant S^2/30 quantum Monte Carlo simulations in order to resolve the controversy. Our main result is for a vacancy in a quantum critical spin-1/2 Heisenberg antiferromagnet on a bilayer lattice. In our susceptibility data for the S=1/2 impurity we observe a Curie constant C=0.262(2). Although the value falls outside the predicted range, it should correspond to an anomalous impurity response, as proposed in Ref. [1]. [1] S. Sachdev, C. Buragohain, and M. Vojta, Science 286, 2479 (1999); M. Vojta, C. Buragohain, and S. Sachdev, Phys. Rev. B 61, 15152 (2000). [2] O. P. Sushkov, Phys. Rev. B 62, 12135 (2000). [3] M. Troyer, Prog. Theor. Phys. Supp. 145, 326 (2002).

  18. The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains

    SciTech Connect

    Fertitta, Edoardo; Paulus, Beate; El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry

    2015-12-28

    The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection S{sub z} has been derived.

  19. Magnetic phase diagram of quasi-2D quantum Heisenberg antiferromagnets with XY anisotropy

    NASA Astrophysics Data System (ADS)

    Xiao, Fan; Landee, Christopher; Turnbull, Mark; Fortune, Nathanael; Hannahs, Scott

    2012-02-01

    The magnetic phase diagram of a quasi-2D quantum Heisenberg antiferromagnetic compound Cu(pz)2(ClO4)2 [1] has been determined by experimental measurements; TN shows a strong field dependence. The data reveal the presence of a small (0.5%) amount of XY anisotropy. QMC simulations have been performed to examine the role of the anisotropy and the interlayer exchange (') upon the phase diagram [2,3]. Comparison of the QMC results with the experimental phase diagram will be presented. [4pt] [1] F. Xiao, F. M. Woodward, C. P. Landee, M. M. Turnbull, C. Mielke, N. Harrison, T. Lancaster, S. J. Blundell, P. J. Baker, P. Babkevich, and F. L. Pratt. Phys. Rev. B, 79(13): 134412 (2009) [0pt] [2] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. B, 68(6):060402 (2003). [0pt] [3] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. Lett., 90(16): 167205 (2003).

  20. Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets

    SciTech Connect

    Radošević, Slobodan M. Pantić, Milan R.; Pavkov-Hrvojević, Milica V.; Kapor, Darko V.

    2013-12-15

    We present the perturbation theory for lattice magnon fields of the D-dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon–magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess–Zumino–Witten term of the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the basis of which we investigate the influence of magnon–magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in low-temperature series for the free energy by examining magnon–magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian). -- Highlights: •Lattice magnon Hamiltonian constructed from the effective Lagrangian. •New Feynman diagrams with colored propagators and vertices for lattice scalar fields. •Influence of magnon–magnon interactions from the WZW term on magnon energies and free energy of O(3) HFM.

  1. Spin wave dynamics in Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes

    NASA Astrophysics Data System (ADS)

    Mi, Bin-Zhou

    2016-09-01

    The spin wave dynamics, including the magnetization, spin wave dispersion relation, and energy level splitting, of Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes are systematically calculated by use of the double-time Green's function method within the random phase approximation. The role of temperature, diameter of the tube, and wave vector on spin wave energy spectrum and energy level splitting are carefully analyzed. There are two categories of spin wave modes, which are quantized and degenerate, and the total number of independent magnon branches is dependent on diameter of the tube, caused by the physical symmetry of nanotubes. Moreover, the number of flat spin wave modes increases with diameter of the tube rising. The spin wave energy and the energy level splitting decrease with temperature rising, and become zero as temperature reaches the critical point. At any temperature, the energy level splitting varies with wave vector, and for a larger wave vector it is smaller. When pb=π, the boundary of first Brillouin zone, spin wave energies are degenerate, and the energy level splittings are zero.

  2. Relief of frustration in the Heisenberg pyrochlore antiferromagnet Gd2Pt2O7

    NASA Astrophysics Data System (ADS)

    Hallas, A. M.; Sharma, A. Z.; Cai, Y.; Munsie, T. J.; Wilson, M. N.; Tachibana, M.; Wiebe, C. R.; Luke, G. M.

    2016-10-01

    The gadolinium pyrochlores Gd2B2O7 are among the best realizations of antiferromagnetically coupled Heisenberg spins on a pyrochlore lattice. We present a magnetic characterization of Gd2Pt2O7 , a unique member of this family. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements show that Gd2Pt2O7 undergoes an antiferromagnetic ordering transition at TN=1.6 K. This transition is strongly first order, as indicated by the sharpness of the heat capacity anomaly, thermal hysteresis in the magnetic susceptibility, and a nondivergent relaxation rate in μ SR . The form of the heat capacity below TN suggests that the ground state is an anisotropic collinear antiferromagnet with an excitation spectrum that is gapped by 0.245(1) meV. The ordering temperature in Gd2Pt2O7,TN=1.6 K, is a substantial 160% increase from other gadolinium pyrochlores, which are all known to order at 1 K or lower. We attribute this enhancement in TN to the B -site cation, platinum. Despite being nonmagnetic, platinum has a filled 5 d t2 g orbital and an empty 5 d eg orbital that can facilitate superexchange. Thus, the magnetic frustration in Gd2Pt2O7 is partially "relieved," thereby promoting magnetic order.

  3. Heisenberg antiferromagnetic chain with multiple spin 1/2 particles of different flavors per site

    NASA Astrophysics Data System (ADS)

    Duki, Solomon F.; Yu, Yi-Kuo

    Motivated by the discoveries of quasi-1D magnetic systems, we studied a quantum mechanical spin lattice system consisting of a one-dimensional antiferromagnetic Heisenberg chain. In this system we considered M spin 1/2 particles of different flavors per site, and the low-lying states, ground state included, of the Hamiltonian was solved numerically using the exact diagonalization method for finite cluster sizes. We have also obtained the corresponding solutions for systems of the same chain length but with one spin M/2 particle per site. The low energy spectra of both systems are then compared. For M = 2 and M =3, our result shows that the two spin chain systems (one spin M/2 per site vs. M spin 1/2 of different flavors per site) have the same excitation spectra at low energy and the number of overlapped states increases as the size of the cluster increases. The observed overlap also indicates that low energy excitations of the M flavored spin 1/2 chain system selects the high spin states, effectively satisfying the Hund's Rule even though the system does not possess the orbital angular momentum. This work was supported by the Intramural Research Program of the National Library of Medicine at the National Institutes of Health.

  4. Multiloop Euler-Heisenberg Lagrangians, Schwinger Pair Creation, and the Photon S-Matrix

    NASA Astrophysics Data System (ADS)

    Huet, I.; de Traubenberg, M. R.; Schubert, C.

    2017-03-01

    Although the perturbation series in quantum electrodynamics has been studied for eighty years concerning its high-order behavior, our present understanding is still poorer than for many other field theories. An interesting case is Schwinger pair creation in a constant electric field, which may possibly provide a window to high loop orders; simple non-perturbative closed-form expressions have been conjectured for the pair creation rate in the weak field limit, for scalar QED in 1982 by Affleck, Alvarez, and Manton, and for spinor QED by Lebedev and Ritus in 1984. Using Borel analysis, these can be used to obtain non-perturbative information on the on-shell renormalized N-photon amplitudes at large N and low energy. This line of reasoning also leads to a number of nontrivial predictions for the effective QED Lagrangian in either four or two dimensions at any loop order, and preliminary results of a calculation of the three-loop Euler-Heisenberg Lagrangian in two dimensions are presented.

  5. Using the ground state of an antiferromagnetic spin-1 atomic condensate for Heisenberg-limited metrology

    NASA Astrophysics Data System (ADS)

    Wu, Ling-Na; You, L.

    2016-03-01

    We show that the ground state of a spin-1 atomic condensate with antiferromagnetic interactions constitutes a useful resource for quantum metrology upon approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, the antiferromagnetic ground-state condensate is a condensate of spin-singlet atom pairs. The inherent correlation between paired atoms allows for parameter estimation at precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by the scaled quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift p to spin-dependent atomic interaction c is studied. At a typical value of p =0.4 c , which corresponds to a magnetic field of 28.6 μ G for c =50 h Hz (for 23Na atom condensate in the F =1 state at a typical density of ˜1014cm-3 ), the scaled QFI can reach ˜0.48 N , which approaches the limit of 0.5 N for the twin-Fock state |N/2 > +|N/2 > - . Our work encourages experimental efforts to reach the ground state of an antiferromagnetic condensate at a extremely low magnetic field.

  6. The ground state of a spin-1 anti-ferromagnetic atomic condensate for Heisenberg limited metrology

    NASA Astrophysics Data System (ADS)

    Wu, Ling-Na; You, Li

    2016-05-01

    The ground state of a spin-1 atomic condensate with anti-ferromagnetic interaction can be applied to quantum metrology approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, atoms in an anti-ferromagnetic ground state condensate exist as spin singlet pairs, whose inherent correlation promises metrological precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift p to spin-dependent atomic interaction c is studied. At a typical value of p = 0 . 4 c corresponding to a magnetic field of 28 . 6 μ G with c = h × 50 Hz (for 23 Na atom condensate in the F = 1 state at a typical density of ~1014cm-3), the scaled QFI can reach ~ 0 . 48 N , which is close to the limits of N for NooN state, or 0 . 5 N for twin-Fock state. We hope our work will stimulate experimental efforts towards reaching the anti-ferromagnetic condensate ground state at extremely low magnetic fields.

  7. Computational quantum chemistry for single Heisenberg spin couplings made simple: Just one spin flip required

    SciTech Connect

    Mayhall, Nicholas J.; Head-Gordon, Martin

    2014-10-07

    We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum S{sup ^}{sub z}, M, to the M − 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M − 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed.

  8. A 1Ds ×1Dc Heisenberg-Kondo Lattice compound Nb12O29

    NASA Astrophysics Data System (ADS)

    Pickett, Warren; Lee, Kwan-Woo

    2015-03-01

    Local moments embedded in conducting systems form a rich platform for unusual phases, with phenomena including Kondo, heavy fermion, and non-Fermi liquid physics. Using first principles based methods and the refined crystal structure based on columns of 3 ×4 planar units of NbO6 octahedra, we determine that mixed valent Nb12O29 displays tightly bound local moments forming spin chains along one direction criss-crossed by conducting ``nanowires'' in the perpendicular direction. Just how local moments - very rare for Nb - emerge and coexist with itinerant electrons, an enigma for decades in this system, is elucidated based on the local structure of the NbO6 octahedra and orbital+spin ordering. The resulting 1Ds ×1Dc Heisenberg-Kondo lattice (s=spin, c=charge) picture will be discussed. NRF-2013R1A1A2A10008946 (K.W.L.), DOE DE-FG02-04ER46111 (W.E.P.).

  9. Critical behavior of the site diluted quantum anisotropic Heisenberg model in two dimensions

    NASA Astrophysics Data System (ADS)

    Lima, L. S.; Pires, A. S. T.; Costa, B. V.

    2015-11-01

    In this work we use the Self Consistent Harmonic Approximation and Quantum Monte Carlo technique to study the Quantum XY on a two dimensional square lattice in the presence of nonmagnetic impurities. In particular we discuss how site disorder changes the Berezinskii-Kosterlitz-Thouless transition temperature, TBKT. This temperature is determined as a function of the nonmagnetic density. Our results are consistent with an anomalous behavior of TBKT at a concentration close to the site percolation threshold. We interpret the results as due to a competition between the confining of vortices and quantum fluctuations, or due to finite size effects.

  10. Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring

    NASA Astrophysics Data System (ADS)

    Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin

    2016-05-01

    In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

  11. Quantum phase transitions and string orders in the spin-1/2 Heisenberg-Ising alternating chain with Dzyaloshinskii-Moriya interaction.

    PubMed

    Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang

    2015-04-29

    Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e. the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e. an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge c = 1; while the rest of the phase transitions in the phase diagram are found to be c = 1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds and find that the even-Haldane phase disappears, but the other three phases, i.e. the AF, AF stripe and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually.

  12. 1 /f α noise and generalized diffusion in random Heisenberg spin systems

    NASA Astrophysics Data System (ADS)

    Agarwal, Kartiek; Demler, Eugene; Martin, Ivar

    2015-11-01

    We study the "flux-noise" spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor Sq(f ) , at finite wave vector q , exhibits a power-law behavior both at high and low frequencies f , with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at T =0 and T =∞ . The low-frequency power-law behavior of the structure factor is inherited by any generic probe with a finite bandwidth and is of the form 1 /fα with 0.5 <α <1 . An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings. More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusion which directly follows from a generalized spin-diffusion propagator. We also argue that 1 /f -noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional 1 /fα behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce 1 /fα noise in SQUIDs.

  13. Description of a Heisenberg ferromagnet above the Curie point as a spin liquid

    NASA Astrophysics Data System (ADS)

    Kuz'min, E. V.

    2005-06-01

    A Heisenberg ferromagnet (F) with spin S=1/2, found in a spin-liquid (SL) state at temperatures above the Curie point τC, is considered. In this spin-liquid state there is no long-range magnetic order but the short-range order is preserved, and the spin correlation functions are isotropic. The spin liquid is described in the framework of a second-order theory by the method of temperature Green functions. The main thermodynamic characteristics of the spin liquid are found as the result of a self-consistent numerical solution of a system of three integral equations. The Curie point τC+, at which the dc magnetic susceptibility at wave vector q=0 diverges, is determined. A comparison of the thermodynamic characteristics of the system in the F state (τ⩽τC, spin-wave theory) and in the SL state (τ⩾τC+) is made. It is shown that τC+>τC, and a modification of spin-wave theory in which τC reaches the value τC+ is indicated. At the point of the F-SL phase transition the spin correlation functions suffer a finite discontinuity, and with increasing temperature they fall off ∝ 1/τ. The heat capacity of the ferromagnet at τ→τC goes to infinity, while in the SL state the heat capacity remains finite at the point τC+ and falls off for τ≫τC+ in proportion to 1/τ2. The susceptibility obeys the Curie-Weiss law.

  14. Instability of a ferrimagnetic state of a frustrated S = 1/2 Heisenberg antiferromagnet in two dimensions

    NASA Astrophysics Data System (ADS)

    Nakano, Hiroki; Sakai, Toru

    2015-03-01

    To clarify the instability of the ferrimagnetism which is the fundamental magnetism of ferrite, numerical-diagonalization study is carried out for the two-dimensional S = 1/2 Heisenberg antiferromagnet with frustration. We find that the ferrimagnetic ground state has the spontaneous magnetization in small frustration; due to a frustrating interaction above a specific strength, the spontaneous magnetization discontinuously vanishes so that the ferrimagnetic state appears only under some magnetic fields. We also find that, when the interaction is increased further, the ferrimagnetism disappears even under magnetic field.

  15. Evaluation of Marsh/Estuarine Water Quality and Ecological Models: An Interim Guide

    DTIC Science & Technology

    1982-01-01

    Simulations," Report R-709-NYC, Rand Corporation , Santa Monica, Calif. Leendertse, J. J., and Liu, S-K. 1975. "A Three Dimensional Model for Estuaries and...Coastal Seas: Vol II - Aspects of Computation," Report 5-1764-OWRT, Rand Corporation , Santa Monica, Calif. • 1977. "A Three Dimensional Model for...Estuaries and Coastal Seas: Vol IV - Turbulent Energy Computation," Report R-2187-OWRT, Rand Corporation , Santa Monica, Calif. Liu, S-K., and Leendertse, J

  16. Field-induced quantum criticality and universal temperature dependence of the magnetization of a spin-1/2 heisenberg chain.

    PubMed

    Kono, Y; Sakakibara, T; Aoyama, C P; Hotta, C; Turnbull, M M; Landee, C P; Takano, Y

    2015-01-23

    High-precision dc magnetization measurements have been made on Cu(C4H4N2) (NO3)2 in magnetic fields up to 14.7 T, slightly above the saturation field Hs=13.97  T, in the temperature range from 0.08 to 15 K. The magnetization curve and differential susceptibility at the lowest temperature show excellent agreement with exact theoretical results for the spin-1/2 Heisenberg antiferromagnet in one dimension. A broad peak is observed in magnetization measured as a function of temperature, signaling a crossover to a low-temperature Tomonaga-Luttinger-liquid regime. With an increasing field, the peak moves gradually to lower temperatures, compressing the regime, and, at Hs, the magnetization exhibits a strong upturn. This quantum critical behavior of the magnetization and that of the specific heat withstand quantitative tests against theory, demonstrating that the material is a practically perfect one-dimensional spin-1/2 Heisenberg antiferromagnet.

  17. Niels Bohr's discussions with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger: the origins of the principles of uncertainty and complementarity

    SciTech Connect

    Mehra, J.

    1987-05-01

    In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger during 1920-1927 are treated. From the formulation of quantum mechanics in 1925-1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory - formulated in fall 1926 by Dirac, London, and Jordan - Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of quantum mechanics and of physical theory as such - formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930 - were continued during the next decades. All these aspects are briefly summarized.

  18. Torque magnetometry study of magnetically ordered state and spin reorientation in the quasi-one-dimensional S =1/2 Heisenberg antiferromagnet CuSb2O6

    NASA Astrophysics Data System (ADS)

    Herak, Mirta; Žilić, Dijana; Matković Čalogović, Dubravka; Berger, Helmuth

    2015-05-01

    The antiferromagnetically ordered state of the monoclinic quasi-one-dimensional S =1 /2 Heisenberg antiferromagnet CuSb2O6 was studied combining torque magnetometry with a phenomenological approach to magnetic anisotropy. This system is known to have a number of different twins in the monoclinic β phase, which differ in the orientation of the two CuO6 octahedra in the unit cell resulting in different orientation of magnetic axes with respect to crystal axes for each twin. We performed torque measurements in magnetic fields H ≤0.8 T on a sample where a certain type of twin was shown to be dominant by ESR spectroscopy. The measured data reveal that the easy axis is the crystallographic b axis for this sample. Phenomenological magnetocrystalline anisotropy energy invariant to crystal symmetry operations was used to model the spin axis direction in zero and finite magnetic fields. Our model reproduces the value of the spin-flop field HSF=1.25 T found in literature. A combination of this approach with our torque results shows that the spin axis will flop in the direction of the maximal value of measured g tensor when the magnetic field H >HSF is applied along the easy axis direction. Our analysis of magnetocrystalline anisotropy energy predicts two possibilities for the easy axis direction in this system, b or a , connected to different crystallographic twins that can be realized in CuSb2O6 . These results offer a possibility to reconcile the different reports of easy axis direction found in literature for this system and also nicely demonstrate how a combination of torque magnetometry and a phenomenological approach to magnetic anisotropy can be used to determine the value of the spin-flop field and the direction of spin axis in antiferromagnets in both H HSF by performing measurements in fields significantly smaller than HSF.

  19. Single-component molecular conductor [Cu(tmdt)(2)] containing an antiferromagnetic Heisenberg chain.

    PubMed

    Zhou, Biao; Yajima, Hiroyuki; Kobayashi, Akiko; Okano, Yoshinori; Tanaka, Hisashi; Kumashiro, Tetsuya; Nishibori, Eiji; Sawa, Hiroshi; Kobayashi, Hayao

    2010-07-19

    Traditional molecular conductors are composed of more than two chemical species and are characterized by low-dimensional electronic band structures. By contrast, the single-component molecular metals [M(tmdt)(2)] (M = Ni, Pt, Au; tmdt = trimethylenetetrathiafulvalenedithiolate) possess three-dimensional electronic structures that can be widely tuned by exchanging the central transition metal atom (M). In this study, the Cu atom was used to realize a new magnetic single-component molecular conductor exhibiting strong pi-d interactions. The crystal structure of [Cu(tmdt)(2)] was found to be essentially the same as those of the Ni, Pt, or Au-based systems with metallic states down to low temperature, but different from the structure of [Cu(dmdt)(2)] (dmdt = dimethyltetrathiafulvalenedithiolate) with its tetrahedrally coordinated dmdt ligands. A compressed pellet of microcrystals exhibited fairly high room-temperature conductivity (sigma(RT) approximately 7 S.cm(-1)), which increased almost linearly with pressure, reaching 110 S.cm(-1) at 15 kbar. This strongly suggests that the single crystal of [Cu(tmdt)(2)] is metallic at high pressure. Magnetic susceptibility measurements indicated one-dimensional Heisenberg behavior with |J| = 117 cm(-1) and an antiferromagnetic transition at 13 K. Density functional theory molecular orbital calculations revealed that the alpha-spin orbital of pdsigma(-) is distributed at the central part of the complex (CuS(4)), and alpha- and beta-sym-Lpi orbitals have almost the same energies and their spins are distributed mainly in the pdsigma(-) orbital. This is in contrast to the first single-component molecular metal [Ni(tmdt)(2)], which has stable metal bands formed from an almost degenerated sym-Lpi orbital (the highest occupied molecular orbital) and asym-Lpi(d) orbital (the lowest unoccupied molecular orbital). These results suggest that the alpha-pdsigma(-) state of [Cu(tmdt)(2)] exists just around the Fermi energy of the virtual

  20. Kristian Camilleri: Heisenberg and the Interpretation of Quantum Mechanics—The Physicist as Philosopher. Cambridge University Press, 2009, ISBN-13:9780521884846, 211 pp.

    NASA Astrophysics Data System (ADS)

    Kleemans, Machiel

    2010-11-01

    The book Heisenberg and the Interpretation of Quantum Mechanics—The Physicist as Philosopher, by Kristian Camilleri is critically reviewed. The work details Heisenberg’s philosophical development from an early positivist commitment towards a later philosophy of language. It is of interest to researchers and graduate students in the history and philosophy of quantum mechanics.

  1. The "Heisenberg's Microscope" as an Example of Using Thought Experiments in Teaching Physics Theories to Students of the Upper Secondary School

    ERIC Educational Resources Information Center

    Velentzas, Athanasios; Halkia, Krystallia

    2011-01-01

    In this work an attempt is made to explore the possible value of using Thought Experiments (TEs) in teaching physics to upper secondary education students. Specifically, a qualitative research project is designed to investigate the extent to which the Thought Experiment (TE) called "Heisenberg's Microscope", as it has been transformed by…

  2. The Heisenberg Microscope: A Powerful Instructional Tool for Promoting Meta-Cognitive and Meta-Scientific Thinking on Quantum Mechanics and the "Nature of Science"

    ERIC Educational Resources Information Center

    Hadzidaki, Pandora

    2008-01-01

    In this paper, we present a multi-dimensional study concerning Heisenberg's "gamma ray microscope", a thought experiment, which is intimately connected with the historical development of quantum mechanics (QM), and also with the most disputed interpretations of quantum theory. In this study: (a) we investigate how philosophers of science read and…

  3. Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

    NASA Astrophysics Data System (ADS)

    Solano-Carrillo, E.; Franco, R.; Silva-Valencia, J.

    2011-06-01

    We study the ground-state and thermal entanglement in the mixed-spin (S,s)=(1,1/2) Heisenberg chain with single-ion anisotropy D using exact diagonalization of small clusters. In this system, a quantum phase transition is revealed to occur at the value D=0, which is the bifurcation point for the global ground state; that is, when the single-ion anisotropy energy is positive, the ground state is unique, whereas when it is negative, the ground state becomes doubly degenerate and the system has the ferrimagnetic long-range order. Using the negativity as a measure of entanglement, we find that a pronounced dip in this quantity, taking place just at the bifurcation point, serves to signal the quantum phase transition. Moreover, we show that the single-ion anisotropy helps to improve the characteristic temperatures above which the quantum behavior disappears.

  4. GENERAL: Thermal entanglement and teleportation of a thermally mixed entangled state of a Heisenberg chain through a Werner state

    NASA Astrophysics Data System (ADS)

    Huang, Li-Yuan; Fang, Mao-Fa

    2008-07-01

    The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.

  5. Coexistence of ferromagnetism and superconductivity close to a quantum phase transition: the Heisenberg- to Ising-type crossover.

    PubMed

    Nevidomskyy, Andriy H

    2005-03-11

    A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analyzed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. A possible explanation of superconductivity in UGe2 is also discussed.

  6. Padé approximations for the magnetic susceptibilities of Heisenberg antiferromagnetic spin chains for various spin values.

    PubMed

    Law, J M; Benner, H; Kremer, R K

    2013-02-13

    The temperature dependence of the spin susceptibilities of S = 1, 3/2, 2, 5/2 and 7/2 Heisenberg antiferromagnetic 1D spins chains with nearest-neighbor coupling was simulated via quantum Monte Carlo calculations, within the reduced temperature range of 0.005 ≤ T* ≤ 100, and fitted to a Padé approximation with deviations between the simulated and fitted data of the same order of magnitude as or smaller than the quantum Monte Carlo simulation error. To demonstrate the practicality of our theoretical findings, we compare these results with the susceptibility of the well known 1D chain compound TMMC ([(CH(3))(4)N[MnCl(3)

  7. Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice.

    PubMed

    Shinaoka, Hiroshi; Tomita, Yusuke; Motome, Yukitoshi

    2011-07-22

    Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate the effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature T(f) is largely enhanced by the spin-lattice coupling and, furthermore, becomes almost independent of Δ in a wide range of the disorder strength Δ. The critical property of the spin-glass transition is indistinguishable from that of the canonical Heisenberg spin glass in the entire range of Δ. These peculiar behaviors are ascribed to a modification of the degenerate manifold from a continuous to semidiscrete one by spin-lattice coupling.

  8. Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters.

    PubMed

    Wang, Ling; Sandvik, Anders W

    2006-09-15

    We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the 2D percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, use quantum Monte Carlo simulations to study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility. Scaling the gap distribution with the cluster length L, Delta approximately L(-), we obtain a dynamic exponent z approximately 2D(f), where D(f)=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast with previous expectations of z=D(f). We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.

  9. Magnetic Signatures of Quantum Critical Points of the Ferrimagnetic Mixed Spin-(1/2, S) Heisenberg Chains at Finite Temperatures

    NASA Astrophysics Data System (ADS)

    Strečka, Jozef; Verkholyak, Taras

    2016-10-01

    Magnetic properties of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zero-temperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped Lieb-Mattis ferrimagnetic phase and Tomonaga-Luttinger spin-liquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zero-temperature quantum critical points through marked local maxima and minima, respectively.

  10. Magnetic Raman Scattering in Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets: Explanation of the Spectral Shape Anomaly

    NASA Astrophysics Data System (ADS)

    Nori, F.; Merlin, R.; Haas, S.; Sandvick, A.; Dagotto, E.

    1996-03-01

    We calculate(F. Nori, R.Merlin, S. Haas, A.W. Sandvik, and E. Dagotto, Physical Review Letters) 75, 553 (1995). the Raman spectrum of the two-dimensional (2D) spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with experiments on various high-Tc precursors, such as La_2CuO4 and YBa_2Cu_3O_6.2. In particular, our calculations reproduce the broad lineshape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden A_1g scattering.

  11. J J THOMSON'S ELECTRON: The Dirac equation. Cosmic implications of a tidy electron

    NASA Astrophysics Data System (ADS)

    Miller, David

    1997-07-01

    Dirac devised the quantum theory of the electron itself, which required him to generalize Schrödinger's famous equation to cover relativistic motion. He interpreted the resulting equation as showing that an antiparticle to the electron must exist.

  12. J. J. Sakurai Prize: Harmony of Scattering Amplitudes: From Gauge Theory to Supergravity

    NASA Astrophysics Data System (ADS)

    Bern, Zvi

    2014-03-01

    As explained in the two previous talks by Lance Dixon and David Kosower, on-shell methods have had an important impact on our understanding of scattering amplitudes and their application to collider physics. In this talk I will describe examples where these ideas have also had impacts in more theoretical areas. The first example shows how these methods have led to the construction of all quantum corrections to specific scattering amplitudes in maximally supersymmetric gauge theory with a large number of color charges. An active area of current research is to do the same for more intricate generic amplitudes of the theory. A second example shows how on-shell methods have uncovered new algebraic structures in gauge-theory amplitudes that have applications to quantum gravity. The advances make it possible to carry out computations in quantum gravity that would have been hopeless with more traditional Feynman diagram methods and to elucidate a remarkable connection between gauge and gravity theories. The results from these investigations have renewed hope that highly supersymmetric gravity theories may be ultraviolet finite, contrary to the prevailing wisdom.

  13. J. J. Sakurai Prize: Scattering Amplitudes - the Story of Loops and Legs

    NASA Astrophysics Data System (ADS)

    Dixon, Lance

    2014-03-01

    Scattering amplitudes are at the interface between quantum field theory and particle experiment. Precise predictions for reactions at energy frontier machines such as the Large Hadron Collider (LHC) rely on quantum corrections to scattering amplitudes involving multiple quarks and gluons, as well as other particles. For decades, theorists used Feynman diagrams for this job. However, Feynman diagrams are just too slow, even on fast computers, to allow adequate precision for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past two decades, alternative methods to Feynman diagrams have come to fruition. The new ``on-shell'' methods are based on the old principle of unitarity. They can be much more efficient because they exploit the underlying simplicity of scattering amplitudes, and recycle lower-loop information. The same methods have also enabled new insight into the structure of gauge theory and gravity at the quantum level, especially in highly supersymmetric theories where they maintain all of the symmetries. I'll give a brief motivation for and introduction to the new methods, which will be followed by descriptions of their phenomenological and formal applications by David Kosower and Zvi Bern.

  14. J. J. Sakurai Prize for Theoretical Particle Physics Talk: The Boundless Horizons of Supercollider Physics

    NASA Astrophysics Data System (ADS)

    Quigg, Chris

    2011-04-01

    The Large Hadron Collider at CERN is moving the experimental frontier of particle physics to the domain of electroweak symmetry breaking, reaching energies around one trillion electron volts for collisions among the basic constituents of matter. We do not know what the new wave of exploration will find, but the discoveries we make and the new puzzles we encounter are certain to change the face of particle physics and echo through neighboring sciences. In this new world, we confidently expect to learn what sets electromagnetism apart from the weak interactions, with profound implications for deceptively simple questions: Why are there atoms? Why chemistry? What makes stable structures possible? A pivotal step will be finding the Higgs boson-or whatever takes its place -and exploring its properties. But we hope for much more. More predictive extensions of the electroweak theory, including dynamical symmetry breaking and supersymmetry, imply new kinds of matter that would be within reach of LHC experiments. We suspect that candidates for the dark matter of the Universe could also await discovery on the TeV scale. The strong interactions may hold their own surprises. As we unravel the riddle of electroweak symmetry breaking, prospects arise for other new insights: into the different forms of matter, the unity of quarks and leptons, and the nature of spacetime. The questions in play all seem linked to one another-and to the kinship of the weak and electromagnetic interactions. I will speak of the evolving dialogue between theory and experiment, highlighting the work before us. Fermilab is operated by the Fermi Research Alliance under contract no. DE-AC02-07CH11359 with the U.S. Department of Energy.

  15. [The history of Spanish neurosurgery: the Valencian school: J.J. Barcia Goyanes].

    PubMed

    Barcia-Mariño, Carlos; Rodríguez-Mena, Ruben

    2013-01-01

    Professor Juan José Barcia-Goyanes started neurosurgical practice from anatomy and neuropsychiatry in response to a vacancy at a department known as "Nervous diseases", in 1931 at Hospital General in Valencia, Spain. Since the first intervention, based on the methods and surgical instruments already used in Europe and the U.S.A., the neurosurgical practice became the mainstay of the department, from which other auxiliary specialties emerged, such as neuroradiology, neurophysiology, neuropathology and also new techniques such as stereotactic surgery, functional neurosurgery and palencephalography. This year, the department celebrates its 80th anniversary. The broad spectrum of Prof. Barcia's scientific work included fields like neurology, neurosurgery and psychiatry, as well as anthropology, medical thought, history of medicine, morphology and history of anatomical language in his work "Onomatologica anatomica nova", in addition to an interesting poetic work. He was a founding member of the Luso-Spanish Neurosurgical Society and the Neurosurgical Society of Levante.

  16. Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds

    NASA Astrophysics Data System (ADS)

    Li, P. H. Y.; Bishop, R. F.; Campbell, C. E.

    2015-01-01

    We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-1/2 J1-J2 Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0 and J2≡κ J1>0 , respectively, in the window 0 ≤κ <1 . The classical version of the model has a single GS phase transition at κcl=1/8 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120∘ Néel order for κ <κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ >κcl . This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ =0 of the spin-1/2 model for the GS energy per spin, E /N =-0.5521 (2 ) J1 , and the GS magnetic order parameter, M =0.198 (5 ) (in units where the classical value is Mcl=1/2), which are among the best available. For the spin-1/2 J1-J2 model we find that the classical transition at κ =κcl is split into two quantum phase transitions at κ1c=0.060 (10 ) and κ2c=0.165 (5 ) . The two quasiclassical AFM states (viz., the 120∘ Néel state and the striped state) are found to be the stable GS phases in the regime κ <κ1c and κ >κ2c , respectively, while in the intermediate regimes κ1c<κ <κ2c the stable GS phase has no evident long-range magnetic order.

  17. Recollections of Physics and of Physicists During the 1920's

    ERIC Educational Resources Information Center

    Dennison, David M.

    1974-01-01

    Presents the author's recollections of the emergence of the new quantum theory and his associations with such men as Oskar Klein, Niels Bohr, Frederick Hund, Werner Heisenberg, J. J. Thomson, and others. (GS)

  18. Semi-Classical Models for Virtual Antiparticle Pairs

    NASA Technical Reports Server (NTRS)

    Batchelor, David; Zukor, Dorothy (Technical Monitor)

    2001-01-01

    Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.

  19. Magnetization Plateau of the S = 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation

    NASA Astrophysics Data System (ADS)

    Hida, K.; Affleck, I.

    The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate \\uparrow\\uparrowdownarrow-type plateau states in the uniform chain, two of them (downarrow\\uparrow\\uparrowdownarrow\\uparrow\\uparrow\\cdots\\ and \\uparrowdownarrow\\uparrow\\uparrowdownarrow\\uparrow\\cdots\\ ) turned out to be robust against the period 3 exchange modulation which favors the bullet-bullet\\uparrowbullet-bullet\\uparrow\\cdots phase up to a critical value of the modulation amplitude (bullet-bullet = singlet dimer) resulting in the Z_2 symmetry broken phase. Another \\uparrow\\uparrowdownarrow-type state with \\uparrow\\uparrowdownarrow\\uparrow\\uparrowdownarrow\\cdots\\ configuration is stabilized for period 3 modulation with opposite sign. The transition between the bullet-bullet\\uparrowbullet-bullet\\uparrow\\cdots\\ -phase and Z_2-broken phase is the Ising transition and that between the \\uparrow\\uparrowdownarrow\\uparrow\\uparrowdownarrow\\cdots\\ -phase and Z_2 broken phase is the first order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.

  20. Symmetry and Bulk-Edge Correspondence in the Dimerized Spin-1/2 Heisenberg Ladder with External Magnetic Field

    NASA Astrophysics Data System (ADS)

    Kariyado, Toshikaze; Hatsugai, Yasuhiro

    2015-03-01

    The dimerized spin-1/2 Heisenberg ladder is topologically characterized from the viewpoints of symmetry protection and bulk-edge correspondence. Our focus is on the plateau phase at the half of the saturation induced by dimerization and magnetic field. The Berry phase associated with the twisted boundary condition is employed as a topological order parameter. The magnetic field reduces the symmetry of the system, but there is a topological phase protected by a spatial inversion symmetry that is characterized by a Berry phase quantized to 0/ π. For a Berry phase quantization, usage of a symmetry-preserving boundary, which leaves at least one inversion center after the system is cut at the boundary, is essential. As a comparison, a symmetry-breaking boundary is also analyzed. Naively, such a boundary is inadequate to make the Berry phase quantized and topological. However, for a specific type of boundary, we found a unique quantization of the Berry phase into +/- π / 2 , instead of 0/ π [1]. Further, for the case of +/- π / 2 -quantization, there appears an edge state distinct from the one for the 0/ π-quantization, which reveals new aspects of the bulk-edge correspondence for symmetry-breaking boundary.

  1. The route to magnetic order in the spin-1/2 kagome Heisenberg antiferromagnet: The role of interlayer coupling

    NASA Astrophysics Data System (ADS)

    Götze, Oliver; Richter, Johannes

    2016-06-01

    While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC J_\\perp , where we study ferro- as well as antiferromagnetic J_\\perp . We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only if the strength of the ILC exceeds about 15% of the intralayer coupling the spin-liquid phase gives way for q = 0 magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, |J^c_\\perp| , is almost independent of the sign of J_\\perp . Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin s, the ILC leads first to a selection of the q = 0 GS. Only at larger |J_\\perp| the ILC drives a first-order transition to the \\sqrt{3}×\\sqrt{3} long-range ordered GS. As a result, the stacked spin-1/2 KHAF exhibits a rich GS phase diagram with two continuous and two discontinuous transitions driven by the ILC.

  2. Magnetism and thermodynamics of the anisotropic frustrated spin-1 Heisenberg antiferromagnet on a body-centered cubic lattice

    NASA Astrophysics Data System (ADS)

    Mi, Bin-Zhou

    2017-02-01

    The magnetic and thermodynamic properties of anisotropic frustrated spin-1 Heisenberg antiferromagnet on a body-centered cubic lattice for Néel phase (the region of weak frustration) are systematically investigated by use of the double-time Green's function method within the random phase approximation and the Anderson and Callen's decoupling. The zero-temperature sublattice magnetization and Néel temperature increase with spin anisotropy strength and single-ion anisotropy strength, and decrease with frustration strength. This indicates that quantum fluctuation is suppressed by spin anisotropy and single-ion anisotropy, by contrast, is strengthened by frustration. It is possible to tune the quantum fluctuations by the competition of anisotropy strength and frustration strength to change the ground state properties of magnetic materials. Although we find that both the spin anisotropy and the single-ion anisotropy suppress the quantum fluctuations, but their respective effects on the thermodynamic quantities, especially the internal energy and free energy, are different at zero temperature and finite temperature. Furthermore, when these two kinds of anisotropic coexist, the effect of the spin anisotropy on the sublattice magnetization and internal energy is larger than that of the single-ion anisotropy.

  3. From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

    NASA Astrophysics Data System (ADS)

    Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric

    2017-02-01

    We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the Néel and tilted Néel states. We apply the quantum transfer matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM’s. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t 0, after which the integral equations have to be modified. In some regimes, t 0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the Néel state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the Néel, tilted Néel and tilted ferromagnet states.

  4. Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

    NASA Astrophysics Data System (ADS)

    Mert, G.; Mert, H. Ş.

    2012-12-01

    The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.

  5. Form factors in quantum integrable models with GL(3)-invariant R-matrix

    NASA Astrophysics Data System (ADS)

    Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.

    2014-04-01

    We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

  6. Neutron diffraction studies of nuclear and magnetic structures in the S=1/2 square Heisenberg antiferromagnets (d{sub 6}-5CAP){sub 2}CuX{sub 4} (X=Br and Cl)

    SciTech Connect

    Coomer, F. C.; Bondah-Jagalu, V.; Grant, K. J.; Harrison, A.; McIntyre, G. J.; Roennow, H. M.; Feyerherm, R.; Wand, T.; Meissner, M.; Visser, D.; McMorrow, D. F.

    2007-03-01

    We report the neutron scattering studies of the nuclear and magnetic structures of deuterated samples of the model two-dimensional S=1/2 Heisenberg antiferromagnets on a square lattice (d{sub 6}-5CAP){sub 2}CuCl{sub 4} and (d{sub 6}-5CAP){sub 2}CuBr{sub 4} (where 5CAP is 2-amino-5-chloropyridinium). Interest in these materials stems from the fact that they have relatively weak exchange between the magnetic ions, and it is therefore possible to perturb their magnetic structures and excitations significantly in experimentally accessible magnetic fields, and thereby access new quantum disordered states. We succeeded in growing fully deuterated single crystals and determined the nuclear and magnetic structures of the bromide at 10 and 1.8 K, respectively, confirming the four-sublattice spin structure expected for systems, where both inter- and intraplane exchange interactions are antiferromagnetic. The determination of the full crystal structure of the bromide highlights the possibility that interlayer exchange may also propagate via hydrogen bonds to and through the 5CAP molecule. We also determined the critical exponents for the sublattice magnetization of the bromide and mapped out the H-T phase diagram of the chloride up to 5 T.

  7. Mathematical Modeling, Simulation, and Control of Physical Processes

    DTIC Science & Technology

    2006-01-01

    are planning Monte Carlo calculations of the macroscopic moment and the the relaxation of these systems, as well as the magnetocaloric effect. A late...important role in the plume dynamics. We are continuing to develop our continuum computational model as well as to experiment with using Monte Carlo ...This is an unusual real world example where the Heisenberg models of magnetic moments have some validity. We are presently modifying an Ising model and

  8. Spin-wave approach for entanglement entropies of the J1-J2 Heisenberg antiferromagnet on the square lattice

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Néel ordered J1-J2 Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the nG=2 Nambu-Goldstone modes give additive logarithmic corrections with a prefactor nG/2 independent of the Rényi index. On the other hand, π /2 corners lead to additional (negative) logarithmic corrections with a prefactor lqc which does depend on both nG and the Rényi index q , in good agreement with scalar field theory predictions. By varying the second neighbor coupling J2 we also explore universality across the Néel ordered side of the phase diagram of the J1-J2 antiferromagnet, from the frustrated side 0

  9. Long-Range Order of the Three-Sublattice Structure in theS=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice

    NASA Astrophysics Data System (ADS)

    Nakano, Hiroki; Todo, Synge; Sakai, Tôru

    2013-04-01

    We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \\simle J_2/J_1 \\le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.

  10. Quantum Monte Carlo study of the itinerant-localized model of strongly correlated electrons: Spin-spin correlation functions

    NASA Astrophysics Data System (ADS)

    Ivantsov, Ilya; Ferraz, Alvaro; Kochetov, Evgenii

    2016-12-01

    We perform quantum Monte Carlo simulations of the itinerant-localized periodic Kondo-Heisenberg model for the underdoped cuprates to calculate the associated spin correlation functions. The strong electron correlations are shown to play a key role in the abrupt destruction of the quasi-long-range antiferromagnetic order in the lightly doped regime.

  11. A Monte-Carlo study for the critical exponents of the three-dimensional O(6) model

    NASA Astrophysics Data System (ADS)

    Loison, D.

    1999-09-01

    Using Wolff's single-cluster Monte-Carlo update algorithm, the three-dimensional O(6)-Heisenberg model on a simple cubic lattice is simulated. With the help of finite size scaling we compute the critical exponents ν, β, γ and η. Our results agree with the field-theory predictions but not so well with the prediction of the series expansions.

  12. Combined analysis of ferromagnetic materials using the Heisenberg Green functions and Ising EFT methods

    NASA Astrophysics Data System (ADS)

    Moujaes, Elie A.; Khater, A.; Abou Ghantous, M.

    2015-10-01

    Ferromagnetic phase diagrams were, for a long time, unsuccessfully determined theoretically, despite the important Callen's 1963 [21] theoretical model. A great variety of experimental data for the magnetization over the entire range of temperature defining the ordered phase compared well with an empirical formula recently determined by Kuz'min (2005) [22]. Nonetheless, the Ising effective field theory (EFT), which can be of enormous support to both methods, was never given attention. The present work intends to show how the Ising EFT technique, when combined with the Green functions in Callen's work, is able to reconcile theoretical work with experimental data. The ratio kTc / JZS(S + 1) plays an important role in finding values for the exchange parameter J, whose first-principles calculation, often depending on the package used, is not properly done. J can be determined for a variety of ferromagnetic materials represented by general spin systems S with a number of nearest neighbours Z and critical temperature Tc, even for models including a percolative feature, characteristic of diluted interactive systems. We demonstrate that EFT is capable of estimating a value of J, which can substitute the use of more complex theoretical models or the performance of ab initio/DFT calculations.

  13. Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions in (2 + 1) dimensions

    NASA Astrophysics Data System (ADS)

    Vasanthi, C. Christal; Latha, M. M.

    2015-11-01

    We study the nonlinear dynamics of (2 + 1) dimensional ferromagnetic (FM) spin system with bilinear and biquadratic interactions in the semiclassical limit and the dynamics is found to be governed by a new integrable fourth order nonlinear Schrödinger (NLS) equation in (2 + 1) dimensions. The integrability is identified by using Lax pair operators and soliton solutions are obtained using straightforward Darboux transformation (DT) technique. The model Hamiltonian representing (2 + 1) dimensional FM spin chain with varying bilinear and biquadratic interactions are also constructed and inhomogeneity effects are studied by performing a perturbation analysis. Moreover, the modulational instability (MI) aspects are discussed through analytical solutions and graphical illustrations.

  14. Niels Bohr's discussions with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger: The origins of the principles of uncertainty and complementarity

    NASA Astrophysics Data System (ADS)

    Mehra, Jagdish

    1987-05-01

    In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger during 1920 1927 are treated. From the formulation of quantum mechanics in 1925 1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory—formulated in fall 1926 by Dirac, London, and Jordan—Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of qnautum mechanics and of physical theory as such—formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930—were continued during the next decades. All these aspects are briefly summarized.

  15. Application of Heisenberg's S matrix program to the angular scattering of the state-to-state F + H2 reaction.

    PubMed

    Shan, Xiao; Connor, J N L

    2014-08-21

    This paper makes two applications of Heisenberg's S matrix program (HSMP) to the differential cross section (DCS) of the benchmark reaction F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 3, mf = 0) + H, at a relative translational energy of 0.119 eV (total energy, 0.3872 eV), where v, j, m are vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. (1) The first application employs a "weak" version of HSMP in which no potential energy surface (PES) is employed. It uses four simple S matrix parametrizations, two of which are piecewise continuous, and two are piecewise discontinuous, developed earlier by X. Shan and J. N. L. Connor (J. Phys. Chem. A 2012, 116, 11414-11426) for the state-to-state H + D2 reaction. We find that the small-angle DCS is reproduced for only θR ≲ 10° when compared with the DCS for a numerical S matrix obtained in a large-scale quantum scattering computation using a PES. Here θR is the reactive scattering angle. (2) In our second application, we ask the question "Can simple modifications to the parametrized S matrix be made in order to extend the agreement to larger angles?" To answer this question, we adopt a "hybrid" version of HSMP, as outlined by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392-8406), which indirectly uses PES information. We make simple Gaussian-type modifications to both the modulus and argument of the S matrix. We then obtain agreement between the DCSs for the modified and numerical S matrices up to θR ≲ 70°, a significant improvement compared with θR ≲ 10° for the unmodified parametrizations. We find that modifying the argument but not the modulus, or modifying the modulus but not the argument, fails to extend the agreement to larger angles. A semiclassical analysis is used to prove that the enhanced small-angle scattering for the "modified-modulus-modified-argument" parametrized S matrix is an example of a forward glory.

  16. OPTICAL PROPERTIES OF ARCTIC MIXED PHASE BOUNDARY LAYER CLOUDS OBSERVED FROM A TETHERED BALLOON INSTRUMENT PLATFORM: PART II a M. Sikand, a J. Koskulics, a K. Stamnes, b B. Hamre, b J.J. Stamnes, c R.P. Lawson a Department of Physics, Stevens Institute of Technology, 1 Castle point, Hoboken, NJ 07030, USA b Department of Physics and Technology, University of Bergen, Allegaten 55, Bergen, Norway c SPEC Incorporated, 3022 Sterling Circle, Suite 200, Boulder, CO 80301, USA

    NASA Astrophysics Data System (ADS)

    Sikand, M. V.; Stamnes, K. H.; Koskulics, J.; Stamnes, J.; Hamre, B.; Lawson, P.

    2011-12-01

    Tethered balloon microphysical and radiative measurements in boundary-layer mixed phase clouds, consisting of ice crystals and liquid droplets, observed in the Arctic have been analyzed. The cloud microphysical and radiometric measurements were collected during a May-June 2008 experimental campaign in Ny Ålesund, Norway, located high in the Arctic at 78.9° N. A state of the art radiative transfer model DISORT is used to analyze the radiometric measurements in order to understand the cloud microphysical properties in mixed phase clouds. The instruments deployed on the tethered balloon system including a radiometer, a cloud particle imager and a meteorological package provide information about the optical properties of mixed phase clouds in the Arctic. These measurements can, therefore, be used to investigate the vertical distribution of the mixed phase arctic clouds. This information will be useful to improve the description of mixed phase clouds in climate models, and thereby reduce the large uncertainty in such models associated with the current lack of data on mixed-phase clouds. The time evolution of cloud optical properties such as cloud optical depth is estimated by using a two layer cloud model based on cloud particle images. Our results show a unique vertical profile of mixed phase clouds as observed on 16 May, 2008 and 29 May, 2008. These results, derived from radiative transfer simulations, show how the vertical distribution of the mixed phase clouds evolves with time. This kind of unique information is difficult to retrieve from satellite observations, which are hampered by low visible contrast between cloud and snow-ice covered surfaces and temperature inversions in the infrared region as well as aircrafts limited by the time of flight. We have found that the mean intensity measured at the balloon is sensitive to the vertical structure of the cloud optical depth. We use the measured mean intensity to estimate the cloud optical depths at 500nm and 800nm

  17. Analysis of quantum spin models on hyperbolic lattices and Bethe lattice

    NASA Astrophysics Data System (ADS)

    Daniška, Michal; Gendiar, Andrej

    2016-04-01

    The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.

  18. Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches.

    PubMed

    Langari, A; Pollmann, F; Siahatgar, M

    2013-10-09

    We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.

  19. Topological Phases of the Spin-1/2 Ferromagnetic--Antiferromagnetic Alternating Heisenberg Chain with Frustrated Next-Nearest-Neighbour Interaction

    NASA Astrophysics Data System (ADS)

    Hida, Kazuo; Takano, Ken'ichi; Suzuki, Hidenori

    2013-06-01

    The spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact solutions with short-range antiferromagnetic correlation on the ferromagnetic--nonmagnetic phase boundary is representative of each spin gap phase.

  20. Super strong nuclear force caused by migrating K̄ mesons - Revival of the Heitler-London-Heisenberg scheme in kaonic nuclear clusters.

    PubMed

    Yamazaki, Toshimitsu; Akaishi, Yoshinori

    2007-06-01

    We have studied the structure of K (-) pp comprehensively by solving this threebody system in a variational method, starting from the Ansatz that the Λ(1405) resonance (≡Λ (*)) is a K (-) p bound state. The structure of K (-) pp reveals a molecular feature, namely, the K (-) in Λ (*) as an "atomic center" plays a key role in producing strong covalent bonding with the other proton. We point out that strongly bound K̄ nuclear systems are formed by "super strong" nuclear force due to migrating real bosonic particles K̄ a la Heitler-London-Heisenberg, whereas the normal nuclear force is caused by mediating virtual mesons. We have shown that the elementary process, p + p → K (+) + Λ (*) + p, which occurs in a short impact parameter and with a large momentum transfer, leads to unusually large self-trapping of Λ (*) by the involved proton, since the Λ (*)-p system exists as a compact doorway state propagating to K (-) pp.