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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

    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

  5. 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.

  6. 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.

  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. 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.

  10. 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

  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. Order-disorder quantum phase transition in the quasi-one-dimensional spin-1/2 collinear antiferromagnetic Heisenberg model.

    PubMed

    Rufo, Sabrina; Mendonça, Griffith; Plascak, J A; de Sousa, J Ricardo

    2013-09-01

    The ground-state properties of the quasi-one-dimensional spin-1/2 antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the x direction are antiferromagnetically coupled with exchange J>0, while spins between chains in the y direction are coupled either ferromagnetically (J' < 0) or antiferromagnetically (J' > 0). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter λ=|J'|/J is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization m_{s} (J' > 0) or a colinear antiferromagnetic magnetization m_{caf} (J' < 0), both behaving as ≃λ¹/² for λ → 0.

  14. 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).

  15. 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.

  16. Global phase diagram of a doped Kitaev-Heisenberg model

    SciTech Connect

    Okamoto, Satoshi

    2013-01-01

    The global phase diagram of a doped Kitaev-Heisenberg model is studied using an $SU(2)$ slave-boson mean-field method. Near the Kitaev limit, $p$-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {\\it et al.} [Phys. Rev. B {\\bf 86}, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a $d$-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another $p$-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This $p$-wave superconducting state does not break the time-reversal symmetry as reported by Hyart {\\it et al.} [Phys. Rev. B {\\bf 85}, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.

  17. 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.

  18. 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.

  19. Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum

    NASA Astrophysics Data System (ADS)

    Mukhin, E.; Tarasov, V.; Varchenko, A.

    2009-05-01

    We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional {mathfrak{gl}_2} -modules. As a byproduct we show that there exist exactly {binom {n}{l}-binom{n}{l-1}} two-dimensional vector subspaces {V subset {mathbb C}[u]} with a basis {f,gin V} such that deg f = l, deg g = n - l + 1 and f ( u) g( u - 1) - f ( u - 1) g( u) = ( u + 1) n .

  20. 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.

  1. 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.

  2. 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.

  3. The spin-1 J1-J3 Heisenberg model on a triangular lattice

    NASA Astrophysics Data System (ADS)

    Rubin, P.; Sherman, A.

    2017-05-01

    Motivated by the experimental data for NiGa2S4, the spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, J1 = -(1 - p)J and J3 = pJ, J > 0, is studied in the range 0 ≤ p ≤ 1. Mori’s projection operator technique and the Lanczos exact diagonalization are used. Mori’s method retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At pcr ≈ 0.2 the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector Q‧ ≈ (1.16, 0) at p ≈ 0.31. With growing p the ordering vector moves along the X axis to the commensurate point Qc = (2π/3, 0) which is reached at p = 1. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the 120° spin structure on each of them. The model is able to describe the state with the incommensurate short-range order observed in NiGa2S4. To verify the used approach the ground state energy and corresponding spin-spin correlations are compared with exact-diagonalization results obtained with the SPINPACK code (the Lanczos exact diagonalization). Results of the two methods are in qualitative agreement.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Spectral Duality Between Heisenberg Chain and Gaudin Model

    NASA Astrophysics Data System (ADS)

    Mironov, Andrei; Morozov, Alexei; Runov, Boris; Zenkevich, Yegor; Zotov, Andrei

    2013-03-01

    In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL k Heisenberg chain is dual to the special reduced k + 2-points gl N Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.

  9. 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.

  10. 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

  11. 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).

  12. 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.

  13. 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).

  14. Density matrix renormalization group study of triangular Kitaev-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Sota, Shigetoshi; Sjinjo, Kazuya; Shirakawa, Tomonori; Tohyama, Takami; Yunoki, Seiji

    2015-03-01

    Topological insulator has been one of the most active subjects in the current condensed matter physics. For most of topological insulators electron correlations are considered to be not essential. However, in the case where electron correlations are strong, novel phases such as a spin liquid phase can emerge in competition with a spin-orbit coupling. Here, using the density matrix renormalization group method, we investigate magnetic phase of a triangular Kitaev-Heisenberg (quantum compass) model that contains a spin-orbital interaction and spin frustration in the antiferromagnetic region. The triangular Kitaev-Heisenberg model is regarded as a dual model of the honeycomb Kitaev-Heisenberg model that is usually employed to discuss A2CuO3 (A=Na, K). Systematically calculating ground state energy, entanglement entropy, entanglement spectrum, and spin-spin correlation functions, we discuss the duality between the triangular and the honeycomb Kitaev-Heisenberg model as well as the ground state magnetic phases.

  15. 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.

  16. Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: a renormalization-group approach.

    PubMed

    Branco, N S; de Sousa, J Ricardo; Ghosh, Angsula

    2008-03-01

    Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.

  17. 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.

  18. Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models

    NASA Astrophysics Data System (ADS)

    Degrazia, G. A.; Rizza, U.; Puhales, F. S.; Welter, G. S.; Acevedo, O. C.; Maldaner, S.

    2012-02-01

    A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical diffusion theory is proposed. This viscosity is described in terms of a velocity variance and a time scale, both associated to the inertial subrange. This new subfilter viscosity contains a cutoff wavenumber kc, presenting an identical form (differing by a constant) to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described in terms of a sharp division between large and small wavenumbers of a turbulent flow and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics of different orders, generated from atmospheric boundary layer simulations employing both Taylor and Heisenberg subfilter viscosities have been compared with observations and results provided by other simulations. The comparison shows that the LES model utilizing the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in different vertical regions of a planetary convective boundary layer (CBL).

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

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

    PubMed

    Yao, Xiaoyan; Dong, Shuai

    2016-05-27

    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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. The Entangled Quantum Heat Engine in the Various Heisenberg Models for a Two-Qubit System

    NASA Astrophysics Data System (ADS)

    Albayrak, Erhan

    2013-05-01

    The four-level entangled quantum heat engine (QHE) is analyzed in the various Heisenberg models for a two-qubit. The QHE is examined for the XX, XXX and XXZ Heisenberg models by introducing a parameter x which controls the strength of the exchange parameter Jz = xJ along the z-axis with respect to the ones along the x- and y-axes, i.e. Jx = Jy = J, respectively. It is assumed that the two-qubit is entangled and in contact with two heat reservoirs at different temperatures and under the effect of a constant magnetic field. The concurrences (C) are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency of the QHE are derived. The contour, i.e. the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are calculated and some interesting features are found.

  16. 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.

  17. 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.

  18. 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 .

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Magnetic order and spin excitations in the Kitaev–Heisenberg model on a honeycomb lattice

    SciTech Connect

    Vladimirov, A. A.; Ihle, D.; Plakida, N. M.

    2016-06-15

    We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev–Heisenberg model proposed for A{sub 2}IrO{sub 3} (A = Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation for four different ordered phases observed in the parameter space of the model: antiferromagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na{sub 2}IrO{sub 3}.

  7. 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.

  8. 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.

  9. Emergent Haldane phase in the S =1 bilinear-biquadratic Heisenberg model on the square lattice

    NASA Astrophysics Data System (ADS)

    Niesen, Ido; Corboz, Philippe

    2017-05-01

    Infinite projected entangled pair states simulations of the S =1 bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and three-sublattice 120∘ magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled S =1 chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.

  10. 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.

  11. J1x-J1y-J2 square-lattice anisotropic Heisenberg model

    NASA Astrophysics Data System (ADS)

    Pires, A. S. T.

    2017-08-01

    The spin one Heisenberg model with an easy-plane single-ion anisotropy and spatially anisotropic nearest-neighbor coupling, frustrated by a next-nearest neighbor interaction, is studied at zero temperature using a SU(3) Schwinger boson formalism (sometimes also referred to as flavor wave theory) in a mean field approximation. The local constraint is enforced by introducing a Lagrange multiplier. The enlarged Hilbert space of S = 1 spins lead to a nematic phase that is ubiquitous to S = 1 spins with single ion anisotropy. The phase diagram shows two magnetically ordered phase, separated by a quantum paramagnetic (nematic) phase.

  12. 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 .

  13. 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.

  14. The Quantum Refrigerator in a Two-Qubit Xxz Heisenberg Model

    NASA Astrophysics Data System (ADS)

    Albayrak, Erhan

    2013-05-01

    The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters Jx = Jy = J and Jz = αJ along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter α is introduced into the model which controls the strength of the exchange parameter Jz in comparison to Jx and Jy, thus, our investigation of QR includes the XX (α = 0.0), XXX (α = 1.0) and XXZ (for other α's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated.

  15. 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.

  16. 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.

  17. 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.

  18. Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

    NASA Astrophysics Data System (ADS)

    Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.

    2014-09-01

    The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.

  19. 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.

  20. 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.

  1. Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

    PubMed Central

    Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.

    2014-01-01

    The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids. PMID:25204626

  2. 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

  3. 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.

  4. 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.

  5. Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model

    NASA Astrophysics Data System (ADS)

    He, Yin-Chen; Zaletel, Michael P.; Oshikawa, Masaki; Pollmann, Frank

    2017-07-01

    The antiferromagnetic spin-1 /2 Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large-scale density matrix renormalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum-dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a π -flux free-fermion model [the parton mean-field ansatz of a U (1 ) Dirac spin liquid].

  6. 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.

  7. Magnetic order in the two-dimensional compass-Heisenberg model

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

    A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, Néel temperature TN, specific heat, and uniform static spin susceptibility χ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of TN on the compass-model interaction is studied. We find that TN is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of χ.

  8. 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.

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

    SciTech Connect

    Pasrija, Kanika Kumar, Sanjeev

    2016-05-06

    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.

  10. 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.

  11. 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.

  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. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  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. Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

    NASA Astrophysics Data System (ADS)

    Huang, Ai-Jun; Wang, Dong; Wang, Jia-Ming; Shi, Jia-Dong; Sun, Wen-Yang; Ye, Liu

    2017-08-01

    In this work, we investigate the quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg XX model with inhomogeneous magnetic field. It has been found that larger coupling strength J between the two spin-chain qubits can effectively reduce the entropic uncertainty. Besides, we observe the mechanics of how the inhomogeneous field influences the uncertainty, and find out that when the inhomogeneous field parameter b<1, the uncertainty will decrease with the decrease of the inhomogeneous field parameter b, conversely, the uncertainty will increase with decreasing b under the condition that b>1. Intriguingly, the entropic uncertainty can shrink to zero when the coupling coefficients are relatively large, while the entropic uncertainty only reduces to 1 with the increase of the homogeneous magnetic field. Additionally, we observe the purity of the state and Bell non-locality and obtain that the entropic uncertainty is anticorrelated with both the purity and Bell non-locality of the evolution state.

  20. 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.

  1. 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.

  2. 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

  3. 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) .

  4. 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.

  5. 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.

  6. 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…

  7. Absence of superconductivity and valence bond order in the Hubbard-Heisenberg model for organic charge-transfer solids.

    PubMed

    Gomes, N; Clay, R T; Mazumdar, S

    2013-09-25

    A frustrated, effective ½-filled band Hubbard-Heisenberg model has been proposed for describing the strongly dimerized charge-transfer solid families κ-(ET)2X and Z[Pd(dmit)2]2. In addition to showing unconventional superconductivity, these materials also exhibit antiferromagnetism, candidate spin-liquid phases, and, in the case of Z=EtMe3P, a spin-gapped phase that has sometimes been referred to as a valence bond solid. We show that neither superconductivity nor the valence bond order phase occurs within the Hubbard-Heisenberg model. We suggest that a description based on ¼-filling, that is reached when the carrier concentration per molecule instead of per dimer is considered, thus may be appropriate.

  8. 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.

  9. 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.

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

    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 hc = 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.

  12. 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.

  13. 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.

  14. Obtaining model parameters for real materials from ab-initio calculations: Heisenberg exchange

    NASA Astrophysics Data System (ADS)

    Korotin, Dmitry; Mazurenko, Vladimir; Anisimov, Vladimir; Streltsov, Sergey

    An approach to compute exchange parameters of the Heisenberg model in plane-wave based methods is presented. This calculation scheme is based on the Green's function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the Néel temperature. Li2MnO3 turns out to be a Slater insulator with antiferromagnetic nearest neighbor exchange defined by the spin splitting. The proposed approach provides a unique way to analyze magnetic interactions, since it allows one to calculate orbital contributions to the total exchange coupling and study the mechanism of the exchange coupling. The work was supported by a grant from the Russian Scientific Foundation (Project No. 14-22-00004).

  15. 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).

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. Z2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Daghofer, Maria; Rousochatzakis, Ioannis; Roessler, Ulrich K.; van den Brink, Jeroen

    2013-03-01

    Investigating the classical Kitaev-Heisenberg Hamiltonian on a triangular lattice, we establish the presence of an incommensurate non-coplanar magnetic phase, which is identified as a lattice of Z2 vortices. The vortices, topological point defects in the SO(3) order parameter of the nearby Heisenberg antiferromagnet, are not thermally excited but due to the spin-orbit coupling and arise at temperature T --> 0 . This Z2-vortex lattice is stable in a parameter regime relevant to iridates. We show that in the other, strongly anisotropic, limit a robust nematic phase emerges. Sponsored by the DFG (Emmy-Noether program).

  1. DETAIL OF CORNERSTONE, WHICH STATES "J.J. DANIELS, BUILDER 1861." NOTE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    DETAIL OF CORNERSTONE, WHICH STATES "J.J. DANIELS, BUILDER 1861." NOTE ALSO IRON STRAP AT EAST CORNER OF ABUTMENT. - Jackson Covered Bridge, Spanning Sugar Creek, CR 775N (Changed from Spanning Sugar Creek), Bloomingdale, Parke County, IN

  2. Entanglement and teleportation through a two-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya interaction

    NASA Astrophysics Data System (ADS)

    Guo, J. L.; Song, H. S.

    2010-01-01

    We study the thermal entanglement in the two-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya (DM) interaction, and teleport an unknown state using the model in thermal equilibrium state as a quantum channel. The effects of DM interaction, including Dx and Dz interaction, the anisotropy and temperature on the entanglement and fully entangled fraction are considered. What deserves mentioning here is that for the antiferromagnetic case, the Dx interaction can be more helpful for increasing the entanglement and critical temperature than Dz, but this cannot for teleportation.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. Impurity Entanglement in the Open-Ended Heisenberg Chains

    NASA Astrophysics Data System (ADS)

    Hu, Ming-Liang

    By using the concept of concurrence, we study pairwise entanglement between the two end spins in the open-ended Heisenberg XXX and XY chains up to ten spins. The results show that by introducing two boundary impurities, one can obtain maximum entanglement at the limit of the impurity parameter |J1| ≪ J for the even-number qubits. When |J1/J| > 0, the entanglement always decreases with the increase in the absolute value of J1/J, and for the Heisenberg XXX chain, C disappears when J1/J exceeds a certain critical point Jic, and attains an asymptotic value C0 when |J1| ≫ J(J1 < 0), while for the Heisenberg XY chain, C always disappears when |J1/J| exceeds a certain critical point Jic. Both C0 and Jic decrease with the increase of the length of the chain.

  10. 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.

  11. 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.

  12. Monte Carlo study of phase transitions and magnetic properties of LaMnO3: Heisenberg model

    NASA Astrophysics Data System (ADS)

    Naji, S.; Benyoussef, A.; El Kenz, A.; Ez-Zahraouy, H.; Loulidi, M.

    2012-08-01

    On the basis of ab initio calculations (FPLO) and Monte Carlo Simulations (MCS) the phase diagrams and magnetic properties of the bulk perovskite LaMnO3 have been studied, using the Heisenberg model. It is shown, using ab initio calculations in the scalar relativistic scheme, that the stable phase is the antiferromagnetic A-type, which corresponds to ferromagnetic order of the manganese ions in the basal planes (a,b) and antiferromagnetic order of these ions between these planes along the c axis. Using the full four-component relativistic scheme, in order to calculate the magnetic anisotropy energy and constants, it is found that the favorable magnetic direction is the (010) b axis. The transition temperatures and the critical exponents are obtained in the framework of Monte Carlo simulations. The magnetic anisotropy and the exchange couplings of the Heisenberg model are deduced from ab initio calculations. They lead, by using Monte Carlo simulations, to a quantitative agreement with the experimental transition temperatures.

  13. [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.

  14. 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.

  15. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas

    2013-11-01

    We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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…

  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. 7. Detail view of 1866 cornerstone (J.J. Havis and M.F. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. Detail view of 1866 cornerstone (J.J. Havis and M.F. Echols, Builders). This cornerstone was moved to the third floor, west elevation of an addition built in 1899. - Riverdale Cotton Mill, Corner of Middle & Lower Streets, Valley, Chambers County, AL

  3. 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.

  4. 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.

  5. Incommensurate phase of a triangular frustrated Heisenberg model studied via Schwinger-boson mean-field theory

    NASA Astrophysics Data System (ADS)

    Li, Peng; Su, Haibin; Dong, Hui-Ning; Shen, Shun-Qing

    2009-08-01

    We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J1 and third-nearest-neighbor interactions J3 by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J3 and varying J1 from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T2 law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa2S4. From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J1≈-3.8755 K and J3≈14.0628 K, in order to account for the experimental data.

  6. 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.

  7. 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.

  8. Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model

    NASA Astrophysics Data System (ADS)

    Xu, Hui-Yun; Yang, Guo-Hui

    2017-09-01

    By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity ( χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J z , Δ or adjust the temperature T to obtain a valid dense coding capacity ( χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.

  9. J. J. Thomson's Atom: A Number of Negatively Electrified Corpuscles Enclosed in a Sphere of Uniform Positive Electrification

    NASA Astrophysics Data System (ADS)

    Barón, MáXimo

    1996-06-01

    During the 1890s many facts regarding the nature of the atom emerged, the most important being that the atom was composed of even smaller particles. Theoretical and experimental discoveries of the time led to the identification of the first subatomic corpuscle, as J. J. Thomson originally called the electron. The measurement of it's e/m ratio, as well as of the properties of cathode rays, opened up a new perspective of the atom and helped to understand several then unexplained phenomena (e.g., atomic spectra). Reluctant to adopt a planetary view, Thomson deliberately chose an electromagnetic approach that has invoked the image of plum puddings and raisin muffins. Although Thomson's model was unsatisfactory for many reasons, it paved the way for Rutherford, one of his brilliant co-workers.

  10. The integrable XXZ Heisenberg model with arbitrary spin: Construction of the Hamiltonian, the ground-state configuration and conformal properties

    NASA Astrophysics Data System (ADS)

    Frahm, Holger; Yu, Nai-Chang; Fowler, Michael

    1990-06-01

    The construction of an integrable generalization of the antiferromagnetic XXZ Heisenberg model with arbitrary spin and easy plane anisotropy is reconsidered. The fusion procedure which has been used to generate models with spin S > {1}/{2} is shown to give hermitian operators corresponding to the physical conserved quantities only in certain (allowed) regions of the anisotropy γ. The forbidden regions coincide with those where Kirillov and Reshetikhin find restrictions on string locations in a formal Bethe ansatz analysis. In each of the allowed regions for the anisotropy there exists a unique ground-state configuration that does not change with γ. The critical behaviour of the S = 1 and S = 2 spin chains is investigated by numerical solution of their associated Bethe ansatz equations. Our results agree with the known decomposition of the spin model into the semidirect product of a free bosonic (gaussian) and a parafermionic ( ZN) theory with N = 2 S in the region of small anisotropy ( γ < π/2 S). They suggest that a similar decomposition holds in certain regions with γ > π/2 S. Here, however, N is given by the integer part of π/γ.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. Surface anisotropy of iron oxide nanoparticles and slabs from first principles: Influence of coatings and ligands as a test of the Heisenberg model

    NASA Astrophysics Data System (ADS)

    Brymora, Katarzyna; Calvayrac, Florent

    2017-07-01

    We performed ab initio computations of the magnetic properties of simple iron oxide clusters and slabs. We considered an iron oxide cluster functionalized by a molecule or glued to a gold cluster of the same size. We also considered a magnetite slab coated by cobalt oxide or a mixture of iron oxide and cobalt oxide. The changes in magnetic behavior were explored using constrained magnetic calculations. A possible value for the surface anisotropy was estimated from the fit of a classical Heisenberg model on ab initio results. The value was found to be compatible with estimations obtained by other means, or inferred from experimental results. The addition of a ligand, coating, or of a metallic nanoparticle to the systems degraded the quality of the description by the Heisenberg Hamiltonian. Proposing a change in the anisotropies allowing for the proportion of each transition atom we could get a much better description of the magnetism of series of hybrid cobalt and iron oxide systems.

  17. 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).

  18. 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).

  19. Detection and characterization of symmetry-broken long-range orders in the spin-1/2 triangular Heisenberg model

    NASA Astrophysics Data System (ADS)

    Saadatmand, S. N.; McCulloch, I. P.

    2017-08-01

    We present new numerical tools to analyze symmetry-broken phases in the context of SU (2 ) -symmetric translation-invariant matrix product states (MPS) and density-matrix renormalization-group (DMRG) methods for infinite cylinders, and determine the phase diagram of the geometrically frustrated triangular Heisenberg model with nearest- and next-nearest-neighbor (NN and NNN) interactions. The appearance of Nambu-Goldstone modes in the excitation spectrum is characterized by "tower of states" levels in the momentum-resolved entanglement spectrum. Symmetry-breaking phase transitions are detected by a combination of the correlation lengths and second and fourth cumulants of the magnetic order parameters (which we call the Binder ratio), even though symmetry implies that the order parameter itself is strictly zero. Using this approach, we have identified a 120∘ order, a columnar order, and an algebraic spin liquid (specific to width-6 systems), alongside the previously studied topological spin liquid phase. For the latter, we also demonstrate robustness against chiral perturbations.

  20. 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.

  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. 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.

  3. 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.

  4. 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.

  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. 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)

  7. 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.

  8. 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.

  9. Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Liu, Chia-Chuan; Goswami, Pallab; Si, Qimiao

    2017-09-01

    Due to the interaction between the topological defects of an order parameter and underlying fermions, the defects can possess induced fermion numbers, leading to several exotic phenomena of fundamental importance to both condensed matter and high-energy physics. One of the intriguing outcomes of induced fermion numbers is the presence of fluctuating competing orders inside the core of a topological defect. In this regard, the interaction between fermions and skyrmion excitations of an antiferromagnetic phase can have important consequences for understanding the global phase diagrams of many condensed matter systems where antiferromagnetism and several singlet orders compete. We critically investigate the relation between fluctuating competing orders and skyrmion excitations of the antiferromagnetic insulating phase of a half-filled Kondo-Heisenberg model on a honeycomb lattice. By combining analytical and numerical methods, we obtain the exact eigenstates of underlying Dirac fermions in the presence of a single skyrmion configuration, which are used for computing the induced chiral charge. Additionally, by employing this nonperturbative eigenbasis, we calculate the susceptibilities of different translational symmetry breaking charges, bond and current density wave orders, and translational symmetry preserving Kondo singlet formations. Based on the computed susceptibilities, we establish spin Peierls and Kondo singlets as dominant competing orders of antiferromagnetism. We show favorable agreement between our findings and field theoretic predictions based on the perturbative gradient expansion scheme, which crucially relies on the adiabatic principle and plane-wave eigenstates for Dirac fermions. The methodology developed here can be applied to many other correlated systems supporting competition between spin-triplet and spin-singlet orders in both lower and higher spatial dimensions.

  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. 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.

  12. 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.

  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 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.

  15. 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.

  16. Chiral spin liquid emerging between competing magnetic order states in the spin-1/2 J1-J2-J3 kagome Heisenberg model

    NASA Astrophysics Data System (ADS)

    Gong, Shoushu; Zhu, Wei; Balents, Leon; Sheng, Dongning

    2015-03-01

    We studied the extended spin- 1 / 2 kagome model with the first neighbor (J1), the second (J2) and third neighbor (J3) couplings using density matrix renormalization group. We established a quantum phase diagram for 0 <= J 2 <= 0 . 25J1 and 0 <=J3 <=J1 , where we find a q = (0 , 0) Neel phase, a chiral spin liquid (CSL), a cuboc1 phase that breaks both time-reversal and spin rotational symmetries, and a valence-bond solid at the neighbor of the Heisenberg model, where a possible Z2 spin liquid has been previously identified. Interestingly, the classical cuboc1 phase could survive in the spin- 1 / 2 system with strong quantum fluctuations, and the CSL emerges between the q = (0 , 0) and the cuboc1 phases. We discover that the CSL has the short spin correlation pattern consistent with the cuboc1 phase, but the chiral order structure is totally different. The CSL might be understood as a result of the competitions between the q = (0 , 0) and the cuboc1 phases in the presence of strong quantum fluctuations. We further studied the quantum phase transitions from the CSL to the magnetically ordered phases, and to the possible Z2 spin liquid of the Heisenberg kagome model. Interestingly, the exotic continuous topological phase transition might be realized in the system.

  17. Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models

    NASA Astrophysics Data System (ADS)

    Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi

    2016-07-01

    Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.

  18. Three-band Hubbard model for Na2IrO3 : Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material

    NASA Astrophysics Data System (ADS)

    Laubach, Manuel; Reuther, Johannes; Thomale, Ronny; Rachel, Stephan

    2017-09-01

    Na2IrO3 was one of the first materials proposed to feature the Kane-Mele-type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Phase diagrams of the corner cubic Heisenberg model and its site-diluted version on a triangular lattice: Renormalization-group treatment

    NASA Astrophysics Data System (ADS)

    Nagai, Kiyoshi

    1985-02-01

    The global phase diagrams of the corner cubic anisotropic discrete-spin Heisenberg (CH) model and its site-diluted version (dCH) on a triangular lattice are investigated through the position-space renormalization-group method of the simple Migdal-Kadanoff type. The two models include many simpler models as their subspaces, and the interrelations among these models are elucidated. The five-dimensional (5D) phase diagram of the dCH model is generated from the 3D one of the CH model by introducing 2D site-dilution operation. The structure of the 5D phase diagram and the effect of site dilution on the CH model are conveniently visualized by introducing the concept of paths in the 3D subspace. The path describes the temperature variation provided that the ratios between the interaction parameters in the original CH model are fixed. The resulting phase diagrams of the dCH model exhibit the typical three-phase coexistence of solid, liquid, and gas, and their qualitative interpretations are summarized.

  11. Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3

    NASA Astrophysics Data System (ADS)

    Chaloupka, Jiří; Khaliullin, Giniyat

    2015-07-01

    We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb-lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which a seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyperhoneycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb-lattice iridates Na2IrO3 and Li2IrO3 , and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.

  12. 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.

  13. 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.

  14. 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.

  15. The spin-1/2 XXZ Heisenberg chain, the quantum algebra Uq[sl(2)], and duality transformations for minimal models

    NASA Astrophysics Data System (ADS)

    Grimm, Uwe; Schütz, Gunter

    1993-06-01

    The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c < 1, including the unitary and nonunitary minimal series. Taking into account the half-integer angular momentum sectors—which correspond to chains with an odd number of sites—in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to new types of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which, however, differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite XXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involving U q [sl(2)] quantum algebra transformations.

  16. SUGRA new inflation with Heisenberg symmetry

    SciTech Connect

    Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch

    2013-10-01

    We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.

  17. 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.

  18. 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.

  19. Spin-wave approach to the two-magnon Raman scattering in a J1 x-J1 y-J2-Jc antiferromagnetic Heisenberg model

    NASA Astrophysics Data System (ADS)

    Liu, Changle; Zhang, Anmin; Zhang, Qingming; Yu, Rong; Wang, Xiaoqun

    2017-03-01

    We study the two-magnon nonresonant Raman scattering in the (π ,π ) and (π ,0 ) in-plane ordered antiferromagnetic phases of a spin-S J1 x-J1 y-J2-Jc Heisenberg model on the tetragonal lattice within the framework of the spin-wave theory. We show that magnon-magnon interactions may significantly change the shape of spectra even in large-S cases. We discuss the effects of various tuning factors to the two-magnon Raman spectra. We find that both the magnetic frustration J2/J1 and the interlayer exchange coupling Jc may significantly affect the spectra in both the B1 g and the A1g ' channels in the (π ,π ) Néel ordered phase. Moreover, we find a splitting of the two-magnon peak in the (π ,0 ) collinear antiferromagnetic phase. We further discuss the implications of our results to the BaMnBi2 and iron pnictide systems.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Static and dynamical spin correlations of the S =1/2 random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

    NASA Astrophysics Data System (ADS)

    Shimokawa, Tokuro; Watanabe, Ken; Kawamura, Hikaru

    2015-10-01

    Inspired by the recent theoretical suggestion that the random-bond S =1 /2 antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this "random-singlet state" might be relevant to the QSL behaviors experimentally observed in triangular organic salts κ -(ET) 2Cu2(CN) 3 and EtMe3Sb [Pd(dmit)2] 2 and in kagome herbertsmithite ZnCu3(OH) 6Cl2 , we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, S (q ) and S (q ,ω ) , by means of an exact diagonalization method. In both triangular and kagome models, the computed S (q ,ω ) in the random-singlet state depends on the wave vector q only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy ω . Especially in the strongly random kagome model, S (q ,ω ) hardly depends on q , and exhibits an almost flat distribution for a wide range of ω , together with a ω =0 peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.

  6. 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.

  7. 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.

  8. Effects of shower spreading on Z degrees yields J J mass resolution

    SciTech Connect

    Wicklund, A.B.

    1991-09-04

    This study concerns the effects of hadronic shower spreading and lateral calorimeter segmentation on the jet-jet mass resolution, for high Pt (Pt>500 GeV) hadronic Z{sup 0} decays. In a previous study, we examined the effects of lateral calorimeter segmentation on detection and measurement of high Pt Z{sup 0} {yields} jet-jet, for an ideal calorimeter with no lateral shower spreading. Other recent studies have also examined the dependence of Z{sup 0} mass resolution on calorimeter segmentation, using more realistic models of shower spreading. The studies reported so far have assumed a common calorimeter segmentation for the EM and HAD compartments, and have concluded that (.05{times}.05) segmentation is a desirable optimization point, given the basic limitations imposed by calorimeter energy resolution, shower size, underlying event, etc. In the present study, we consider the case that HAD is segmented more coarsely, specifically (.1{times}.1) instead of (.05{times}.05), and we assume that the EM segmentation is fixed at (.05{times}.05), as driven by electron identification requirements. This hybrid segmentation'' would represent a significant cost saving for SDC. We might expect that the effects of coarser HAD segmentation on the jet- jet mass resolution would be minimal for two reasons. First, roughly half the jet energy is deposited in the EM compartment anyway, and benefits from the (.05{times}.05) EM cell size. Second, the lateral hadron shower size increases with depth, so that the shower spreading is larger on average in the HAD calorimeter alone, than it is in EM + HAD combined. Thus we might expect coarser segmentation to be less important deeper in the calorimeter.

  9. 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.

  10. 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.

  11. The topological basis expression of Heisenberg spin chain

    NASA Astrophysics Data System (ADS)

    Hu, Taotao; Ren, Hang; Xue, Kang

    2013-11-01

    In this paper, it is shown that the Heisenberg XY, XXZ, XXX, and Ising model all can be constructed from the Braid group algebra generator and the Temperley-Lieb algebra generator. And a new set of topological basis expression is presented. Through acting on the different subspaces, we get the new nontrivial six-dimensional and four-dimensional Braid group matrix representations and Temperley-Lieb matrix representations. The eigenstates of Heisenberg model can be described by the combination of the set of topological bases. It is worth mentioning that the ground state is closely related to parameter q which is the meaningful topological parameter.

  12. Quantum Monte Carlo study of the spin-1/2 honeycomb Heisenberg model with mixed antiferromagnetic and ferromagnetic interactions in external magnetic fields

    NASA Astrophysics Data System (ADS)

    Huang, Yi-Zhen; Su, Gang

    2017-05-01

    The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling J >0 and ferromagnetic (F) coupling J'<0 along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling J' between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the x y plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with J >0 , J'<0 and J <0 , J'>0 are obtained to be ν =0.70046 (1 ) and 0.7086 (3 ) , respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and γ /ν are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.

  13. Competition between spin liquids and valence-bond order in the frustrated spin-1/2 Heisenberg model on the honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Ferrari, Francesco; Bieri, Samuel; Becca, Federico

    2017-09-01

    Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor J1 and second-neighbor J2 antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio J2/J1 , we find strong evidence for a continuous transition to a nonmagnetic phase at J2/J1≈0.23 . Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For 0.23 ≲J2/J1≲0.36 , a gapless Z2 spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the Néel order melts, this ordered state becomes clearly favored only for J2/J1≳0.3 . Finally, for 0.36 ≲J2/J1≤0.5 , a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the Néel antiferromagnet from the plaquette valence-bond solid.

  14. 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.

  15. Magnetic susceptibilities of rectangular Heisenberg S=1/2 antiferromagnets

    NASA Astrophysics Data System (ADS)

    Valleau, Tom; Butcher, Rob; Keith, Brian; Landee, Christopher; Turnbull, Mark; Sandvik, Anders

    2008-03-01

    Rectangular antiferromagnets are two-dimensional systems with inequivalent exchange strengths (J', J) along the two principle axes with J' ≡ αJ, α <1. They have an intermediate dimensionality that can vary continuously from 1D (α = 0 ) to square 2D (α = 1). There exist a number of physical realizations of rectangular antiferromagnets (CuPzBr2, CuPzCl2, CuPz(N3)2 where Pz = pyrazine) but there has been no previous mechanism for interpreting their susceptibilities in terms of two exchange parameters. We have simulated the susceptibility of the rectangular S=1/2 Heisenberg antiferromagnet using the stochastic series expansion quantum Monte Carlo method [1] and used the results to interpret our experimental data. For example, copper pyrazine diazide, CuPz(N3)2, has a primary exchange of 15.5 K and an anisotropy parameter α = 0.4. The stronger exchange is due to the superexchange pathway through the pyrazine molecule and the weaker corresponds to the azide bridges. [1] A. Sandvik, PRB 59, R14157 (1999).

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. Covalent bonding and J-J mixing effects on the EPR parameters of Er3 + ions in GaN crystal

    NASA Astrophysics Data System (ADS)

    Rui-Peng, Chai; Long, Li; Liang, Liang; Qing, Pang

    2016-07-01

    The EPR parameters of trivalent Er3+ ions doped in hexagonal GaN crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er3+ ion and the replaced Ga3+ ion apart from the intrinsic covalency of host GaN. Furthermore, the J-J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J-J mixing contribution is from the manifold 2K15/2, which accounts for about 2.5%. The next important J-J contribution arises from the crystal-field mixture between the ground state 4I15/2 and the first excited state 4I13/2, and is usually less than 0.2%. The contributions from the rest states may be ignored. Project supported by the Foundation of Education Department of Shaanxi Province, China (Grant No. 16JK1461).

  4. 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.

  5. 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).

  6. 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.

  7. 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...

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

    NASA Astrophysics Data System (ADS)

    Pan, Yu; Amini, Hadis; Miao, Zibo; Gough, John; Ugrinovskii, Valery; James, Matthew R.

    2014-06-01

    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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  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. Studies of magnetocaloric effect on spin-1/2 J{sub 1}-J{sub 2} Heisenberg hexagons

    SciTech Connect

    Deb, Moumita Ghosh, Asim Kumar

    2016-05-06

    Magnetocaloric effect of four different spin-1/2 J{sub 1}-J{sub 2} Heisenberg hexagons has been studied in terms of adiabatic demagnetization. Four hexagons with different combinations of antiferromagnetic and ferromagnetic Heisenberg exchange interactions are considered. Level of frustration on those models is different. Studies on the magnetization process, nature of isentrops and properties of magnetocaloric effect have been carried out. Comparison of results on those models has been discussed.

  16. 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.

  17. 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.

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

    PubMed

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

    2013-01-01

    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. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.?

  4. 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.

  5. 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.

  6. 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)

  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. Integrable hierarchies of Heisenberg ferromagnet equation

    NASA Astrophysics Data System (ADS)

    Nugmanova, G.; Azimkhanova, A.

    2016-08-01

    In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.

  9. Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment

    NASA Astrophysics Data System (ADS)

    Catana, Catalin; GuÅ£ǎ, Mǎdǎlin

    2014-07-01

    Finding optimal and noise robust probe states is a key problem in quantum metrology. In this paper we propose Markov dynamics as a possible mechanism for generating such states, and show how the Heisenberg scaling emerges for systems with multiple "dynamical phases" (stationary states), and noiseless channels. We model noisy channels by coupling the Markov output to "environment" ancillas, and consider the scenario where the environment is monitored to increase the quantum Fisher information of the output. In this setup we find that the survival of the Heisenberg limit depends on whether the environment receives "which phase" information about the memory system.

  10. Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

    NASA Astrophysics Data System (ADS)

    Groha, Stefan; Essler, Fabian H. L.

    2017-08-01

    Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-defined excitations even though integrability is broken.

  11. 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.

  12. 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.

  13. 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.

  14. Unifying decoherence and the Heisenberg Principle

    NASA Astrophysics Data System (ADS)

    Janssens, Bas

    2017-03-01

    We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality and the disturbance caused on the measured system. Finally, the third inequality provides a sharp lower bound on the amount of decoherence in terms of the measurement quality. This gives a unified description of both the Heisenberg uncertainty principle and the collapse of the wave function.

  15. 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.

  16. 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

  17. Unifying decoherence and the Heisenberg Principle

    NASA Astrophysics Data System (ADS)

    Janssens, Bas

    2017-08-01

    We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality and the disturbance caused on the measured system. Finally, the third inequality provides a sharp lower bound on the amount of decoherence in terms of the measurement quality. This gives a unified description of both the Heisenberg uncertainty principle and the collapse of the wave function.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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…

  6. 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…

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Propagation and jamming dynamics in Heisenberg spin ladders

    NASA Astrophysics Data System (ADS)

    Krimphoff, Carlo B.; Haque, Masudul; Läuchli, Andreas M.

    2017-04-01

    We investigate the propagation dynamics of initially localized excitations in spin-1/2 Heisenberg ladders. We consider initial states with two overturned spins, either on neighboring sites on the same leg or on the two sites of a single rung, in an otherwise polarized (ferromagnetic) background. Compared to the corresponding dynamics in a chain (single leg), we observe several additional modes of propagation. We connect these propagation modes to features of the spectrum of the ladder system, and to different effective models corresponding to different segments of the spectrum. In addition to the regular propagation modes, we observe for one mode a peculiar "jamming" dynamics where components of the excitations remain localized in an unusual manner. A comparison with the spin-1 bilinear-biquadratic chain is developed and explored, where a similar phenomenon is shown to occur.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Full counting statistics in the spin-1/2 Heisenberg XXZ chain

    NASA Astrophysics Data System (ADS)

    Collura, Mario; Essler, Fabian H. L.; Groha, Stefan

    2017-10-01

    The spin-1/2 Heisenberg chain exhibits a quantum critical regime characterized by quasi long-range magnetic order at zero temperature. We quantify the strength of quantum fluctuations in the ground state by determining the probability distributions of the components of the (staggered) subsystem magnetization. Some of these exhibit scaling and the corresponding universal scaling functions can be determined by free fermion methods and by exploiting a relation with the boundary sine-Gordon model.

  19. Ground states, magnetization plateaus and bipartite entanglement of frustrated spin-1/2 Ising-Heisenberg and Heisenberg triangular tubes

    NASA Astrophysics Data System (ADS)

    Alécio, Raphael C.; Lyra, Marcelo L.; Strečka, Jozef

    2016-11-01

    The ground-state phase diagram, magnetization process and bipartite entanglement of the frustrated spin-1/2 Ising-Heisenberg and Heisenberg triangular tube (three-leg ladder) are investigated in a non-zero external magnetic field. The exact ground-state phase diagram of the spin-1/2 Ising-Heisenberg tube with Heisenberg intra-rung and Ising inter-rung couplings consists of six distinct gapped phases, which manifest themselves in a magnetization curve as intermediate plateaus at zero, one-third and two-thirds of the saturation magnetization. Four out of six available ground states exhibit quantum entanglement between two spins from the same triangular unit evidenced by a non-zero concurrence. Density-matrix renormalization group calculations are used in order to construct the ground-state phase diagram of the analogous but purely quantum spin-1/2 Heisenberg tube with Heisenberg intra- and inter-rung couplings, which consists of four gapped and three gapless phases. The Heisenberg tube shows a continuous change of the magnetization instead of a plateau at zero magnetization, while the intermediate one-third and two-thirds plateaus may be present or not in the zero-temperature magnetization curve.

  20. 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.

  1. Spin dynamics simulations of two-dimensional clusters with Heisenberg and dipole-dipole interactions.

    PubMed

    Depondt, Ph; Mertens, F G

    2009-08-19

    Spin dynamics with the Landau-Lifshitz equation has provided topics for a wealth of research endeavors. We introduce here a numerical integration method which explicitly uses the precession motion of a spin about the local field, thus intrinsically conserving spin lengths, and therefore allowing for relatively quick results for a large number of situations with varying temperatures and couplings. This method is applied to the effect of long-range dipole-dipole interactions in two-dimensional clusters of spins with nearest-neighbor XY-Heisenberg exchange interactions on a square lattice at finite temperature. The structures thus obtained are analyzed through orientational correlations functions. Magnon dispersion curves, different from those of the standard Heisenberg model, are obtained and discussed. The number of vortices in the system is discussed as a function of temperature and typical examples of vortex dynamics are shown.

  2. 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)

  3. 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)

  4. 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.

  5. 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

  6. 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.

  7. First-Order Polynomial Heisenberg Algebras and Coherent States

    NASA Astrophysics Data System (ADS)

    Castillo-Celeita, M.; Fernández C, D. J.

    2016-03-01

    The polynomial Heisenberg algebras (PHA) are deformations of the Heisenberg- Weyl algebra characterizing the underlying symmetry of the supersymmetric partners of the Harmonic oscillator. When looking for the simplest system ruled by PHA, however, we end up with the harmonic oscillator. In this paper we are going to realize the first-order PHA through the harmonic oscillator. The associated coherent states will be also constructed, which turn out to be the well known even and odd coherent states.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains.

    PubMed

    Liu, Wanguo; Shen, Yang; Fang, Guisheng; Jin, Chongjun

    2016-05-18

    A mechanism for realizing nonreciprocal elementary excitation of spin wave (SW) is proposed. We study a reference model which describes a magnonic crystal (MC) formed by two Heisenberg chains with a lateral displacement (dislocation) and a longitudinal spacer, and derive a criterion to judge whether the elementary excitation spectra are reciprocal in this ferromagnetic lattice. An analytical method based on the spin precession equation is used to solve the elementary excitation spectra. The solution is related to a key factor, the spatio-temporal structure factor [Formula: see text], which can be directly calculated through the structural parameters. When it keeps invariant under the reversions of the external magnetic field [Formula: see text] and the dislocation [Formula: see text], or one of them, the spectra are reciprocal. Otherwise, the SW possesses nonreciprocal spectra with direction-dependent band edges and exhibits a directional magnetoresistance effect. This criterion can be regarded as a necessary and sufficient condition for the (non)reciprocity in the spin lattice. Besides, this novel lattice provides a prototype for spin diodes and spin logic gates.

  15. Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains

    NASA Astrophysics Data System (ADS)

    Liu, Wanguo; Shen, Yang; Fang, Guisheng; Jin, Chongjun

    2016-05-01

    A mechanism for realizing nonreciprocal elementary excitation of spin wave (SW) is proposed. We study a reference model which describes a magnonic crystal (MC) formed by two Heisenberg chains with a lateral displacement (dislocation) and a longitudinal spacer, and derive a criterion to judge whether the elementary excitation spectra are reciprocal in this ferromagnetic lattice. An analytical method based on the spin precession equation is used to solve the elementary excitation spectra. The solution is related to a key factor, the spatio-temporal structure factor {θk}≤ft(Δ x,B\\right) , which can be directly calculated through the structural parameters. When it keeps invariant under the reversions of the external magnetic field B and the dislocation Δ x , or one of them, the spectra are reciprocal. Otherwise, the SW possesses nonreciprocal spectra with direction-dependent band edges and exhibits a directional magnetoresistance effect. This criterion can be regarded as a necessary and sufficient condition for the (non)reciprocity in the spin lattice. Besides, this novel lattice provides a prototype for spin diodes and spin logic gates.

  16. Exact Diagonalization studies of frustrated AFM Heisenberg polytopes

    NASA Astrophysics Data System (ADS)

    Rousochatzakis, Ioannis; Laeuchli, Andreas; Mila, Frederic

    2007-03-01

    We explore the low energy physics of the AFM s=1/2 Heisenberg model on a number of frustrated magnetic molecule systems using exact diagonalization (ED). Particular emphasis is given to molecules with spins occupying the vertices of symmetric polyhedra. To this end, we have extended the standard ED technique in order to exploit the full point group (permutation) symmetry, thus including higher than one-dimensional irreducible representations. Apart from classifying the energy spectra according to both spin and permutation symmetries, our method provides the exact level degeneracies. In particular, for large frustrated polytopes, we find the existence of an accordingly large number of low-lying singlets below the first triplet, similarly to the case of frustrated 2D magnets. We also study the properties of the local spectral density functions, in view of interpreting recent neutron scattering experiments in Fe30, one of the biggest AFM frustrated molecule available (comprising 30 spins 5/2 mounted on the vertices of a icosidodecahedron).

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD

    NASA Astrophysics Data System (ADS)

    Pérez-García, David; Tierz, Miguel

    2014-04-01

    By using random matrix models, we uncover a connection between the low-energy sector of four-dimensional QCD at finite volume and the Heisenberg XX model in a 1D spin chain. This connection allows us to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. For the spin chain, we predict a third-order phase transition and a Tracy-Widom law in the transition region. We also comment on possible numerical implications of the connection as well as on possible experimental implementations.

  2. 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.

  3. Toward Heisenberg-limited spectroscopy with multiparticle entangled states.

    PubMed

    Leibfried, D; Barrett, M D; Schaetz, T; Britton, J; Chiaverini, J; Itano, W M; Jost, J D; Langer, C; Wineland, D J

    2004-06-04

    The precision in spectroscopy of any quantum system is fundamentally limited by the Heisenberg uncertainty relation for energy and time. For N systems, this limit requires that they be in a quantum-mechanically entangled state. We describe a scalable method of spectroscopy that can potentially take full advantage of entanglement to reach the Heisenberg limit and has the practical advantage that the spectroscopic information is transferred to states with optimal protection against readout noise. We demonstrate our method experimentally with three beryllium ions. The spectroscopic sensitivity attained is 1.45(2) times as high as that of a perfect experiment with three non-entangled particles.

  4. 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.

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. Fourier and Schur-Weyl transforms applied to XXX Heisenberg magnet

    NASA Astrophysics Data System (ADS)

    Jakubczyk, P.; Lulek, T.; Jakubczyk, D.; Lulek, B.

    2010-03-01

    Similarities and differences between Fourier and Schur-Weyl transforms have been discussed in the context of a one-dimensional Heisenberg magnetic ring with N nodes. We demonstrate that main difference between them correspond to another partitioning of the Hilbert space of the magnet. In particular, we point out that application of the quantum Fourier transform corresponds to splitting of the Hilbert space of the model into subspaces associated with the orbits of the cyclic group, whereas, the Schur-Weyl transform corresponds to splitting into subspaces associated with orbits of the symmetric group.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Thermodynamics of the Heisenberg ferromagnet in an applied magnetic field.

    NASA Technical Reports Server (NTRS)

    Flax, L.

    1972-01-01

    The anisotropic-Heisenberg-ferromagnet formalism developed previously is examined to include an applied magnetic field for the isotropic case in the random-phase approximation. Thermodynamic quantities such as magnetization, susceptibility, and the derivative of magnetization with respect to temperature are studied near the Curie point.

  15. 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.

  16. Spin-1 Heisenberg ferromagnet using pair approximation method

    SciTech Connect

    Mert, Murat; Mert, Gülistan; Kılıç, Ahmet

    2016-06-08

    Thermodynamic properties for Heisenberg ferromagnet with spin-1 on the simple cubic lattice have been calculated using pair approximation method. We introduce the single-ion anisotropy and the next-nearest-neighbor exchange interaction. We found that for negative single-ion anisotropy parameter, the internal energy is positive and heat capacity has two peaks.

  17. 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.

  18. 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.

  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

    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.

  1. 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.

  2. 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.

  3. Deformed Heisenberg algebra, fractional spin fields, and supersymmetry without fermions

    SciTech Connect

    Plyushchay, M.S.

    1996-02-01

    Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [{ital a}{sup {minus}},{ital a}{sup +}]=1+{nu}{ital K}, involving the Klein operator {ital K}, {l_brace}{ital K},{ital a}{sup {plus_minus}}{r_brace}=0, {ital K}{sup 2}=1. The connection of the minimal set of equations with the earlier proposed {open_quote}{open_quote}universal{close_quote}{close_quote} vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of exact and spontaneously broken {ital N}=2 supersymmetry allowing us to realize a Bose{endash}Fermi transformation and spin-1/2 representation of SU(2) group in terms of one bosonic oscillator. The construction admits an extension to the case of OSp(2{parallel}2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. The possibility of {open_quote}{open_quote}superimposing{close_quote}{close_quote} the two applications of the DHA for constructing a supersymmetric (2+1)-dimensional anyon system is discussed. As a consequential result we point out that the {ital osp}(2{parallel}2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model. Copyright {copyright} 1996 Academic Press, Inc.

  4. 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.

  5. Partial Ferrimagnetism in S = 1/2 Heisenberg Ladders with a Ferromagnetic Leg, an Antiferromagnetic Leg, and Antiferromagnetic Rungs

    NASA Astrophysics Data System (ADS)

    Sekiguchi, Kazutaka; Hida, Kazuo

    2017-08-01

    Ground-state and finite-temperature properties of S = 1/2 Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear σ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga-Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as T-2 in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  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. 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.

  12. 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.

  13. 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.

  14. Large-N theory of the Sp(N) Heisenberg quantum antiferromagnet on an anisotropic triangular lattice

    NASA Astrophysics Data System (ADS)

    Chung, Chung-Hou; Marston, Brad

    2000-03-01

    The magnetic properties of the two-dimensional layered organic superconductors κ-(BEDT-TTF)_2X are modeled by a spin-1/2 Heisenberg quantum antiferromagnet on an anisotropic triangular lattice. The phase diagram is ascertained by means of a large-N expansion of the Sp(N) generalization of the physical SU(2) \\cong Sp(1) Heisenberg magnet.(S. Sachdev and N. Reed, Int. J. Mod. Phys. B5), 219 (1991). The phase diagram is presented in the two-dimensional parameter space of J_1/J_2, the ratio of the nearest to next-nearest neighbor Heisenberg exchange, and the ratio nb / N, which sets the strength of the quantum fluctuations. At large nb / N (equivalent to the large-spin limit of the physical SU(2) model) quantum effects are small, the ground states break global Sp(N) spin-rotational symmetry, and exhibit magnetic long-range-order (LRO). At small nb / N, however, quantum fluctuations overwhelm the tendency to order and there is only short-range magnetic order (SRO). The LRO and SRO phases can be further classified into two types depending on the size of the anisotropy: (i) ground states with commensurate, collinear, spin correlations; and (ii) ground states with incommensurate, coplanar, spin correlations. Finite-N corrections due to a Berry's phase term modify the character of the SRO phases, leading in the case of the commensurate state to spin-Peierls order and the confinement of spinons.

  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. 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.

  17. Heisenberg-limited sensitivity with decoherence-enhanced measurements.

    PubMed

    Braun, Daniel; Martin, John

    2011-01-01

    Quantum-enhanced measurements use quantum mechanical effects to enhance the sensitivity of the measurement of classical quantities, such as the length of an optical cavity. The major goal is to beat the standard quantum limit (SQL), that is, an uncertainty of order , where N is the number of quantum resources (for example, the number of photons or atoms used), and to achieve a scaling 1/N, known as the Heisenberg limit. So far very few experiments have demonstrated an improvement over the SQL. The required quantum states are generally highly entangled, difficult to produce, and very prone to decoherence. Here, we show that Heisenberg-limited measurements can be achieved without the use of entangled states by coupling the quantum resources to a common environment that can be measured at least in part. The method is robust under decoherence, and in fact the parameter dependence of collective decoherence itself can be used to reach a 1/N scaling.

  18. 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.

  19. 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.

  20. q-graded Heisenberg algebras and deformed supersymmetries

    SciTech Connect

    Ben Geloun, Joseph; Hounkonnou, Mahouton Norbert

    2010-02-15

    The notion of q-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for q complex number in the unit disk. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary Z{sub 2} grading or Grassmann parity for associative superalgebra and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit q{yields}-1 for which the Arik and Coon deformation [J. Math. Phys. 17, 524 (1976)] of the Heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. [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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. Magnetic Properties of a Heisenberg Coupled-Trimer Molecular Magnet: General

    SciTech Connect

    Haraldsen, Jason T; Barnes, Ted {F E }; Sinclair IV, John W; Thompson, James R; Sacci, Robert L.; Turner, John F. C.

    2009-01-01

    We report predictions for the energy eigenstates and inelastic neutron scattering excitations of an isotropic Heisenberg hexamer consisting of general spin S and S′ trimers. Specializing to spin-1/2 ions, we give analytic results for the energy excitations, magnetic susceptibility, and inelastic neutron scattering intensities for this hexamer system. To examine this model further, we compare these calculations to the measured magnetic susceptibility of a vanadium material, which is considered to be well defined magnetically as an isolated S = 1/2 V4+ trimer model. Using our model, we determine the amount of inter-trimer coupling that can be accommodated by the measured susceptibility, and predict the inelastic neutron scattering spectrum for comparison with future measurements.

  13. Magnetic properties of copper pyrazine bridged quasi two dimensional quantum Heisenberg antiferromagnetic (QHAF) compounds

    NASA Astrophysics Data System (ADS)

    Xiao, Fan

    The magnetic properties of a family of molecular-based quasi-two-dimensional S=1/2 Heisenberg antiferromagnets (2D QHAF) are studied. Three compounds, Cu(pz)2 (ClO4)2, Cu(pz)2(BF 4)2, and [Cu(pz)2(NO3)](PF6) contain similar planes of Cu2+ ions linked into magnetically square lattices by bridging pyrazine molecules (pz =C4H4N 2). The anions provide charge balance as well as isolation between the layers. Low field single crystal measurements of susceptibility and magnetization reveal low ratios of Neel temperatures to exchange strengths (4.25/17.5 = 0.243, 3.80/15.3 = 0.248, and 3.05/10.8 = 0.282, respectively) while the ratio of the anisotropy fields HA(kOe) to the saturation field HSAT(kOe) are small (2.6/490 = 5.3x10-3, 2.4/430 = 5.5x10-3, and 0.07/300 = 2.3x10-4, respectively), demonstrating close approximations to a two-dimensional Heisenberg model. The susceptibilities of Cu(pz)2(ClO4)2 and Cu(pz)2(BF4)2 show evidence of a spin crossover (Heisenberg to XY) at low temperatures; their zero-field ordering transitions are primarily driven by the XY behavior with the ultimate three-dimensional transition appearing parasitically. The [Cu(pz)2(NO 3)](PF6) compound remains Heisenberg-like at all temperatures, with its transition to the Neel state due to the inter- layer interactions. High field single crystal measurements of Cu(pz)2(ClO 4)2 indicates that both spin crossover transition temperature and ordering temperature increase as the external field increases up to 5 T. The results suggests a field-induced XY anisotropy is produced by the external field and the ordering temperature vs field follows a Berezinskii-Kosterlitz-Thouless (BKT)-like transition trend predicted by quantum Monte Carlo simulation. Calorimetry measurements were performed to verify the hypothesis with external fields up to 33 T. The results successfully confirmed our prediction. The transition temperature shows a rounded maximum at 16 T and starts dropping as the field gets stronger. The

  14. MnCl2ṡH2O: A quasi-one-dimensional Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    DeFotis, G. C.; Wiese, R. S.; Scherrer, C. W.

    1990-05-01

    The magnetic properties of MnCl2ṡH2O, a heretofore unexamined hydrate of manganese dichloride, have been studied. The behavior is clearly distinguishable from that of the anhydrous material or either the dihydrate or the tetrahydrate. At high temperatures the susceptibility is Curie-Weiss-like, with a Weiss constant θ=-4.9±0.3 K in χM=C/(T-θ); this may be compared with the values θ=-3.3 K for the anhydrous material, -14.5±0.3 K for the dihydrate (as determined in this work), and -1.8 K for the tetrahydrate. Departures from linearity occur below 20 K, and a broad maximum in the powder susceptibility appears at T(χmax)=3.60±0.10 K with χmax=0.304±0.003 emu/mol. The susceptibility drops sharply below 2.23 K, and ∂χ/∂T is a maximum at 2.16±0.01 K, which is identified with the Néel temperature Tc. Certain features of the data suggest two-dimensional Heisenberg model behavior, for example the ratios Tc/‖θ‖=0.44 and Tc/T(χmax)=0.60. However, fits to χ(T) using a high-temperature series expansion for the S=5/2 two-dimensional square planar Heisenberg model are unconvincing, as are similar attempts based on a three-dimensional model. In contrast, the model of a classical Heisenberg antiferromagnetic spin chain scaled to S=5/2 permits an excellent fit, with J/k=-0.49±0.04 K the intrachain exchange (in Ĥex=-2J∑i> jŜiṡŜ j). An interchain exchange of ‖J'/k‖=0.015±0.004 K, probably antiferromagnetic, can also be inferred, from the antiferromagnetic transition at Tc =2.16 K. The intrachain exchange is very similar to that in MnCl2ṡ2H2O, while the interchain exchange is much weaker.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Open Heisenberg chain under boundary fields: A magnonic logic gate

    NASA Astrophysics Data System (ADS)

    Landi, Gabriel T.; Karevski, Dragi

    2015-05-01

    We study the spin transport in the quantum Heisenberg spin chain subject to boundary magnetic fields and driven out of equilibrium by Lindblad dissipators. An exact solution is given in terms of matrix product states, which allows us to calculate exactly the spin current for any chain size. It is found that the system undergoes a discontinuous spin-valve-like quantum phase transition from ballistic to subdiffusive spin current, depending on the value of the boundary fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate operating with the boundary fields as the base element.

  2. 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.

  3. 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.

  4. 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.

  5. Magnetization and isothermal magnetic entropy change of a mixed spin-1 and spin-2 Heisenberg superlattice

    NASA Astrophysics Data System (ADS)

    Xu, Ping; Du, An

    2017-09-01

    A superlattice composed of spin-1 and spin-2 with ABAB … structure was described with Heisenberg model. The magnetizations and magnetic entropy changes under different magnetic fields were calculated by the Green's function method. The magnetization compensation phenomenon could be observed by altering the intralayer exchange interactions and the single-ion anisotropies of spins. Along with the temperature increasing, the system in the absence of magnetization compensation shows normal magnetic entropy change and displays a peak near the critical temperature, and yet the system with magnetization compensation shows normal magnetic entropy change near the compensation temperature but inverse magnetic entropy change near the critical temperature. Finally, we illustrated the reasons of different behaviors of magnetic entropy change by analyzing the contributions of two sublattices to the total magnetic entropy change.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

    2017-05-01

    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.

  12. 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.

  13. Universal Quantum Gates for Quantum Computation on Magnetic Systems Ruled by Heisenberg-Ising Interactions

    NASA Astrophysics Data System (ADS)

    Delgado, F.

    2017-05-01

    The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating classical computer gates. As for optical as well as magnetic systems, those gates are obtained as quantum evolutions. Despite, in certain cases they are attained as an asymptotic series of evolution effects. The current work exploits the direct sum of the evolution operator on a non-local basis for the driven bipartite Heisenberg-Ising model to construct a set of equivalent universal gates as straight evolutions for this interaction. The prescriptions to get these gates are reported as well as a general procedure to evaluate their performance.

  14. On Hopf algebroid structure of κ-deformed Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Lukierski, J.; Škoda, Z.; Woronowicz, M.

    2017-05-01

    The (4 + 4)-dimensional κ-deformed quantum phase space as well as its (10 + 10)-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the (10 + 10)-dimensional quantum phase space is the double of D = 4 κ-deformed Poincaré Hopf algebra H and the standard (4 + 4)-dimensional space is its subalgebra generated by κ-Minkowski coordinates \\widehat {{x_μ }} and corresponding commuting momenta \\widehat {{p_μ }}. Every Heisenberg double appears as the total algebra of a Hopf algebroid over a base algebra which is in our case the coordinate sector. We exhibit the details of this structure, namely the corresponding right bialgebroid and the antipode map. We rely on algebraic methods of calculation in Majid-Ruegg bicrossproduct basis. The target map is derived from a formula by J.-H. Lu. The coproduct takes values in the bimodule tensor product over a base, what is expressed as the presence of coproduct gauge freedom.

  15. 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 | → + ∞.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. Investigation of thermodynamic properties of Cu(NH3)4SO4·H2O, a Heisenberg spin chain compound

    NASA Astrophysics Data System (ADS)

    Chakraborty, Tanmoy; Singh, Harkirat; Chaudhuri, Dipanjan; Jeevan, Hirale S.; Gegenwart, Philipp; Mitra, Chiranjib

    2017-10-01

    Detailed experimental investigation of thermal and magnetic properties are presented for Cu(NH3)4SO4·H2O, an ideal uniform Heisenberg spin ½ chain compound. A comparison of these properties with relevant spin models is also presented. Temperature dependent magnetic susceptibility and specific heat data have been compared with the exact solution for uniform Heisenberg chain model derived by means of Bethe ansatz technique. Magnetization isotherms measured as a function of field are analyzed using the numerical results simulated by Quantum Monte Carlo technique. Specific heat as a function of magnetic field (up to 7T) and temperature (down to 2 K) is reported. Subsequently, the data are compared with the corresponding theoretical curves for infinite Heisenberg spin ½ chain model with J = 6 K. Moreover, internal energy and entropy are calculated by analyzing the experimental specific heat data. Magnetic field and temperature dependent behavior of entropy and internal energy are in good agreement with the theoretical predictions.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. Optimal uncertainty relations in a modified Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Abdelkhalek, Kais; Chemissany, Wissam; Fiedler, Leander; Mangano, Gianpiero; Schwonnek, René

    2016-12-01

    Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.

  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. 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

  10. 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.

  11. 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.

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

    SciTech Connect

    Deb, Moumita Ghosh, Asim Kumar

    2016-05-23

    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 Cu{sub 3}WO{sub 6}.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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)

  3. 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.

  4. 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

  5. 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.

  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. 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.

  8. 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.

  9. On foundational thinking in fundamental physics, from Riemann to Einstein to Heisenberg

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2012-03-01

    This paper considers the nature of foundational thinking in fundamental physics, most especially in quantum mechanics. By "fundamental physics" I mean those areas of experimental and theoretical physics that deal with the ultimate constitution of nature, for example, as defined by the so-called elementary particles in the case of quantum physics. By "foundational thinking" I mean thinking that concerns fundamental physics itself. First, I argue, following Riemann, that our foundational thinking is based on hypotheses that we form and test. Second, I argue that foundational thinking in physics is defined by concepts, and that in modern physics foundational concepts always contains physical, mathematical, and philosophical components. Third, finally, I argue that the relationships between these components and, hence, our foundational thinking, are different in quantum mechanics than they are in classical physics and relativity. In these theories mathematics describes, by way of idealized models, physical reality, and predictions made by them are derived from these descriptions. By contrast, in quantum mechanics, mathematics only serves to predict the outcome of quantum experiments in the absence of any description, however idealized, of quantum objects and their behavior. At least such is the case in certain interpretations of quantum mechanics, which follow and develop Heisenberg's approach in his paper introducing quantum mechanics, as does, for example, Bohr's interpretation, known as complementarity.

  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. 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.

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

    PubMed

    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. 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.

  14. 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.

  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. 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)

  17. 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.

  18. Heisenberg's error-disturbance uncertainty relation: Experimental study of competing approaches

    NASA Astrophysics Data System (ADS)

    Sulyok, Georg; Sponar, Stephan

    2017-08-01

    Over the past few years, Heisenberg's error-disturbance uncertainty relation has experienced increased attention since several experimental publications verified the theoretical findings of Ozawa predicting the violation and thus necessary reformulation of Heisenberg's relation. However, soon after their appearance, an alternative theory was presented by Busch and co-workers, which proclaimed the validity of Heisenberg's relation and thus gave rise to heated debates. Here, we present an experimental comparison of the competing approaches by applying them to the same neutron optical measurement apparatus. Empirical results for the different definitions of error and disturbance are presented for special input states and configurations of the apparatus to illustrate the opposing approaches. The inequalities restricting errors and disturbances are particularly emphasized. Despite the strong controversy, in the case of projectively measured qubit observables, both approaches lead to equal outcomes.

  19. 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.

  20. 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.

  1. Black hole solutions in Euler-Heisenberg theory

    NASA Astrophysics Data System (ADS)

    Yajima, Hiroki; Tamaki, Takashi

    2001-03-01

    We construct static and spherically symmetric black hole solutions in the Einstein-Euler-Heisenberg (EEH) system which is considered as an effective action of a superstring theory. We consider electrically charged, magnetically charged, and dyon solutions. We can solve analytically for the magnetically charged case. We find that they have some remarkable properties about causality and black hole thermodynamics depending on the coupling constant of the EH theory a and b, though they have a central singularity as in the Schwarzschild black hole. We restrict a>0 because it is natural if we think of EH theory as a low-energy limit of the Born-Infeld (BI) theory. (i) For the magnetically charged case, whether or not the extreme solution exists depends on the critical parameter a=acrit. For a<=acrit, there is an extreme solution as in the Reissner-Nortström (RN) solution. The main difference from the RN solution is that there appear solutions below the horizon radius of the extreme solution and they exist till rH-->0. Moreover, for a>acrit, there is no extreme solution. For arbitrary a, the temperature diverges in the rH-->0 limit. (ii) For the electrically charged case, the inner horizon appears under some critical mass M0 and the extreme solution always exists. The lower limit of the horizon radius decreases when the coupling constant a increases. (iii) For the dyon case, we expect a variety of properties because of the term b(ɛμνρσFμνFρσ)2 which is peculiar to the EH theory. But their properties are mainly decided by the combination of the parameters a+8b. We show that solutions have similar properties to the magnetically charged case in the rH-->0 limit for a+8b<=0. For a+8b>0, it depends on the parameters a,b.

  2. 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

  3. 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.

  4. 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.

  5. 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'|.

  6. On the interplay between symmetry breaking, integrability, and chaos in the semiclassical limit of the Heisenberg system.

    PubMed

    Pellegrino, G. Q.; Furuya, K.; Nemes, M. C.

    1995-06-01

    In this work we present a detailed numerical analysis of the interplay between symmetry breaking, integrability, and chaos in the two- and three-spin Heisenberg models. The results suggest that a very simple and powerful tool to convey such information are the plots of the energy level spacings Delta(n) versus the energy level index n, together with the correlation plots Delta(n+1)xDelta(n). When integrability is broken, these plots are shown to identify very sharply an energy below which one has chaotic behavior. The particularly strong point in favor of such analysis is that it can be useful in partially chaotic regimes. (c) 1995 American Institute of Physics.

  7. 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.

  8. 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.

  9. 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.

  10. Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field

    NASA Astrophysics Data System (ADS)

    Wang, Dong; Huang, Aijun; Ming, Fei; Sun, Wenyang; Lu, Heping; Liu, Chengcheng; Ye, Liu

    2017-06-01

    The uncertainty principle provides a nontrivial bound to expose the precision for the outcome of the measurement on a pair of incompatible observables in a quantum system. Therefore, it is of essential importance for quantum precision measurement in the area of quantum information processing. Herein, we investigate quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a two-qubit Heisenberg \\boldsymbol{X}\\boldsymbol{Y}\\boldsymbol{Z} spin chain. Specifically, we observe the dynamics of QMA-EUR in a realistic model there are two correlated sites linked by a thermal entanglement in the spin chain with an inhomogeneous magnetic field. It turns out that the temperature, the external inhomogeneous magnetic field and the field inhomogeneity can lift the uncertainty of the measurement due to the reduction of the thermal entanglement, and explicitly higher temperature, stronger magnetic field or larger inhomogeneity of the field can result in inflation of the uncertainty. Besides, it is found that there exists distinct dynamical behaviors of the uncertainty for ferromagnetism \\boldsymbol{}≤ft(\\boldsymbol{J}<\\boldsymbol{0}\\right) and antiferromagnetism \\boldsymbol{}≤ft(\\boldsymbol{J}>\\boldsymbol{0}\\right) chains. Moreover, we also verify that the measuring uncertainty is dramatically anti-correlated with the purity of the bipartite spin system, the greater purity can result in the reduction of the measuring uncertainty, vice versa. Therefore, our observations might provide a better understanding of the dynamics of the entropic uncertainty in the Heisenberg spin chain, and thus shed light on quantum precision measurement in the framework of versatile systems, particularly solid states.

  11. 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.

  12. 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.

  13. 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.

  14. 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…

  15. 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…

  16. 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

  17. Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

    NASA Astrophysics Data System (ADS)

    Blessy, B. S. Gnana; Latha, M. M.

    2017-10-01

    We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

  18. Numerical calculations for Heisenberg ferromagnet on honeycomb lattice using Oguchi’s method

    SciTech Connect

    Mert, Gülistan; Mert, H. Şevki

    2015-03-10

    Magnetic properties such as the magnetization, internal energy and specific heat for Heisenberg ferromagnet with spin - 1/2 on honeycomb lattice are have been calculated using Oguchi’s method. We have found that the magnetic specific heat exhibits two peaks.

  19. Von Neumann algebras, affiliated operators and representations of the Heisenberg relation

    NASA Astrophysics Data System (ADS)

    Liu, Zhe

    Von Neumann algebras are self-adjoint, strong-operator closed subalgebras (containing the identity operator) of the algebra of all bounded operators on a Hilbert space. Factors are von Neumann algebras whose centers consist of scalar multiples of the identity operator. In this thesis, we study unbounded operators affiliated with finite von Neumann algebras, in particular, factors of Type II1. Such unbounded operators permit all the formal algebraic manipulations used by the founders of quantum mechanics in their mathematical formulation, and surprisingly, they form an algebra. The operators affiliated with an infinite von Neumann algebra never form such an algebra. The Heisenberg commutation relation, QP -- PQ = --ihI , is the most fundamental relation of quantum mechanics. Heisenberg's encoding of the ad-hoc quantum rules in this simple relation embodies the characteristic indeterminacy and uncertainty of quantum theory. Representations of the Heisenberg relation in various mathematical structures are discussed. In particular, we answer the question --- whether the Heisenberg relation can be realized with unbounded operators in the algebra of operators affiliated with a factor of type II1.

  20. A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra

    NASA Astrophysics Data System (ADS)

    Takaesu, Toshimitsu

    2011-07-01

    In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated.

  1. 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.

  2. 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.

  3. Low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets

    NASA Astrophysics Data System (ADS)

    Wang, Ling; Sandvik, Anders W.

    2010-02-01

    We study the low-energy dynamics of S=1/2 antiferromagnetic Heisenberg clusters constructed by diluting a square lattice at vacancy concentration p at and below the percolation threshold p∗≈0.407 . The finite-size scaling behavior of the average excitation gap, ⟨Δ⟩˜L-z , where L is the cluster length, is obtained using quantum Monte Carlo results for an upper bound Δ∗ to Δ , derived from sum rules. At the percolation threshold, we obtain a dynamic exponent z=3.6±0.1≈2Df for clusters with singlet (S=0) ground state. Here Df=91/48 is the fractal dimensionality of the percolating cluster. We argue that this large dynamic exponent—roughly twice that expected for quantum-rotor excitations—is a consequence of weakly interacting localized effective magnetic moments, which form due to local sublattice imbalance. This picture is supported by an extremal-value analysis of local spectral gaps, which delivers an exponent relation (between z and two exponents characterizing the local-gap distribution) reproduced by our simulation data. However, the average ⟨Δ∗⟩ over all clusters, which have mostly ground-state spin S>0 , scales with a smaller exponent than for the S=0 clusters alone; z≈1.5Df . Lanczos exact diagonalization for small clusters show that typically, S→S-1 in the lowest-energy excitations while the dominant spectral weight originates from S→S+1 excitations. Thus, the scaling of ⟨Δ∗⟩ for clusters with ground state S>0 does not reflect the lowest-energy excitations but the higher S→S+1 excitations. This result can be understood within a valence bond picture. To further explore the scenario of localized moments, we introduce a classical dimer-monomer aggregation model to study the distribution of nearest-neighbor sites forming dimers (which are the objects used in mapping to the quantum-rotor model) and unpaired spins (monomers). The monomers are localized and, thus, effective magnetic moments should form in the spin system

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Papageorgiou, G.; Schroers, B. J.

    2010-11-01

    We define a theory of Galilean gravity in 2+ 1 dimensions with cosmological constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke group, extending our previous study of classical and quantum gravity in 2+ 1 dimensions in the Galilean limit. We exhibit an r-matrix which is compatible with our Chern-Simons action (in a sense to be defined) and show that the associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the classical double of the extended Heisenberg algebra. We deduce that, in the quantisation of the theory according to the combinatorial quantisation programme, much of the quantum theory is determined by the quantum double of the extended q-deformed Heisenberg algebra.

  9. Circumventing Heisenberg's Uncertainty Principle in Atom Interferometry Tests of the Equivalence Principle

    NASA Astrophysics Data System (ADS)

    Roura, Albert

    2017-04-01

    Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenberg's uncertainty principle. We present a promising scheme that overcomes these problems by compensating the effects of the gravity gradients and circumvents the fundamental limitations due to Heisenberg's uncertainty principle. Furthermore, it relaxes the experimental requirements on initial colocation by several orders of magnitude.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Optical probe of Heisenberg-Kitaev magnetism in α -RuCl3

    NASA Astrophysics Data System (ADS)

    Sandilands, Luke J.; Sohn, C. H.; Park, H. J.; Kim, So Yeun; Kim, K. W.; Sears, Jennifer A.; Kim, Young-June; Noh, Tae Won

    2016-11-01

    We report a temperature-dependent optical spectroscopic study of the Heisenberg-Kitaev magnet α -RuCl3 . Our measurements reveal anomalies in the optical response near the magnetic ordering temperature. At higher temperatures, we observe a redistribution of spectral weight over a broad energy range that is associated with nearest-neighbor spin-spin correlations. This finding is consistent with highly frustrated magnetic interactions and in agreement with theoretical expectations for this class of material. The optical data also reveal significant electron-hole interaction effects, including a bound excitonic state. These results demonstrate a clear coupling between charge and spin degrees of freedom and provide insight into the properties of thermally disordered Heisenberg-Kitaev magnets.

  16. 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

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

    SciTech Connect

    Fu, M.; Imai, T.; Han, T. -H.; Lee, Y. S.

    2015-11-05

    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 ckagome, 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 ckagome that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.

  18. A representation of Weyl-Heisenberg Lie algebra in the quaternionic setting

    NASA Astrophysics Data System (ADS)

    Muraleetharan, B.; Thirulogasanthar, K.; Sabadini, I.

    2017-10-01

    Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of quaternions and on a quaternionic slice, namely on a copy of the complex plane inside the quaternions. For the quaternionic harmonic oscillator, the uncertainty relation is shown to saturate on a neighborhood of the origin in the case we consider the whole set of quaternions, while it is saturated on the whole slice in the case we take the slice-wise approach. In analogy with the complex Weyl-Heisenberg Lie algebra, Lie algebraic structures are developed for the quaternionic case. Finally, we introduce a quaternionic displacement operator which is square integrable, irreducible and unitary, and we study its properties.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Spin-glass transition in Heisenberg spin system with ± J random bonds

    NASA Astrophysics Data System (ADS)

    Ghazali, A.; Lallemand, P.; Diep, H. T.

    1986-02-01

    We investigate by Monte Carlo simulations the simple cubic lattice with Heisenberg spins interacting via short range ± J random bonds for different antiferromagnetic bond concentrations x. We find that for x<0.25, a transition of the para-ferromagnetic type occurs. For 0.25⪅ x⩽0.5, the existence of a remanant magnetization and of a rounded peak of the specific heat together with other data support a paramagnetic-spin-glass transition at finite temperature.

  5. Spin ordering in a random antiferromagnetic Heisenberg spin system: Numerical simulation

    NASA Astrophysics Data System (ADS)

    Ghazali, A.; Diep, Hung T.

    1985-04-01

    We study by a Monte Carlo method, a three-dimensional classical antiferromagnetic random Heisenberg spin system with an exchange interaction which decreases exponentially with distance. We find no indication of a spin glass transition when only isotropic exchange exists. However, a gradual spin freezing is observed as T→0. In the presence of a strong enough Ising-type uniaxial magnetic anisotropy, we observe a peak in the specific heat and a stable order parameter. However, no true thermoremanent magnetization is observed.

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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).

  12. 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.

  13. Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet

    NASA Astrophysics Data System (ADS)

    Bera, A. K.; Lake, B.; Essler, F. H. L.; Vanderstraeten, L.; Hubig, C.; Schollwöck, U.; Islam, A. T. M. N.; Schneidewind, A.; Quintero-Castro, D. L.

    2017-08-01

    Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and, as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain spatially anisotropic magnetic insulators. These can be thought of in terms of weakly coupled chains of spins S =1 /2 , and a spin flip thus carries integer spin S =1 . The collective excitations in these systems, called spinons, turn out to carry fractional spin quantum number S =1 /2 . Interestingly, at sufficiently low temperatures the weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinon-confinement process in the quasi-one-dimensional, spin-1/2 antiferromagnet with Heisenberg-Ising (XXZ) anisotropy SrCo2V2O8 . A wide temperature range both above and below the long-range ordering temperature TN=5.2 K is explored. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. These are based on a description in terms of a one-dimensional, S =1 /2 XXZ antiferromagnetic spin chain, where the interchain couplings are modeled by an effective staggered magnetic mean field. A wide range of exchange anisotropies are investigated and the parameters specific to SrCo2V2O8 are identified. Recently developed theoretical technique based on tangent-space matrix product states gives a very

  14. 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.

  15. 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.

  16. Diversity of quantum ground states and quantum phase transitions of a spin-1/2 Heisenberg octahedral chain

    NASA Astrophysics Data System (ADS)

    Strečka, Jozef; Richter, Johannes; Derzhko, Oleg; Verkholyak, Taras; Karľová, Katarína

    2017-06-01

    The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED), and density-matrix renormalization group (DMRG) methods. The model belongs to the class of flatband systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase, and two different spin-liquid phases. If the intraplaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of the parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifths, and three-fifths of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in the vicinity of discontinuous quantum phase transitions.

  17. 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.

  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. 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.

  20. 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-

  1. 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.

  2. 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.

  3. 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.

  4. Mobile holes in a two-dimensional Heisenberg antiferromagnet

    NASA Astrophysics Data System (ADS)

    Itoh, Toshihiro; Arai, Masao; Fujiwara, Takeo

    1990-09-01

    Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as √20 × √20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (+/-π/2,+/-π/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''<~0.

  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. 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

  8. 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

  9. Intrinsic viscosities of polyelectrolytes: determination and modeling of the effects of extra salt.

    PubMed

    Eich, Andreas; Wolf, Bernhard A

    2011-10-24

    Based on early measurements of J. J. Hermans and co-workers (D. T. F. Pals, J. J. Hermans, Recl. Trav. Chim. Pays-Bas 1952, 71, 513-520; D. T. F. Pals, J. J. Hermans, J. Polym. Sci. 1950, 5, 733-734; D. T. F. Pals, J. J. Hermans, J. Polym. Sci. 1948, 3, 897-898), the present contribution demonstrates how primary data should be evaluated in order to obtain reliable intrinsic viscosities. This procedure yields detailed information on the changes of the intrinsic viscosities and of the corresponding viscometric interaction parameters caused by an increasing salinity of water. Both quantities decline from a maximum value in the pure solvent to a minimum value, which is approached in the limit of sufficiently high salt concentrations, and can be modeled quantitatively by means of a Boltzmann sigmoid. Particular attention is paid to the significance of results obtained by means of the method of isoionic dilution, proposed by J. J. Hermans and co-workers. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  10. 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.

  11. Relations between quantum correlations, purity and teleportation fidelity for the two-qubit Heisenberg XYZ system

    NASA Astrophysics Data System (ADS)

    Qin, Meng; Li, Yan-Biao; Wu, Fang-Ping

    2014-07-01

    Quantifying and understanding quantum correlations may give a direct reply for many issues regarding the interesting behaviors of quantum system. To explore the quantum correlations in quantum teleportation, we have used a two-qubit Heisenberg XYZ system with spin-orbit interaction as a quantum channel to teleport an unknown state. By using different measures and standard teleportation protocols, we have derived the analytical expressions for quantum discord, entanglement of formation, purity, and maximal teleportation fidelity of the system. We compare their different characteristics and analyze the relationships between these quantities.

  12. 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.

  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. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.