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Bao J, Shen L, Liu H, Guo B, Sun Z. Nonlocality of mixtures of the ground and first excited states withinJ1-J2Heisenberg model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:445403. [PMID: 39059435 DOI: 10.1088/1361-648x/ad682a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2024] [Accepted: 07/26/2024] [Indexed: 07/28/2024]
Abstract
We investigate both bipartite and multipartite nonlocality in theJ1-J2Heisenberg model. Bipartite nonlocality is measured by the Clauser-Horne-Shimony-Holt inequality, while multipartite nonlocality is explored through Bell-type inequalities. Our findings reveal that neither ground-state nor full thermal-state nonlocality reliably characterizes quantum phase transitions (QPTs). However, we uncover that the mixed-state nonlocality of the ground and first excited states exhibits distinctive characteristics applicable to both bipartite and multipartite scenarios. We also demonstrate how mixed-state quantum correlation behaviors depend on varying temperature regimes. In the bipartite case, we observe a phenomenon known as 'correlation reversal' with increasing temperature, a previously unreported occurrence in other models. For the multipartite case, the ability to signify phase transitions is significantly enhanced as the temperature rises. Furthermore, we discover a linear scaling effect that provides valuable insights for extrapolating QPTs in the thermodynamic limit asN→∞. Additionally, we identify the critical temperature at which mixed-state nonlocality becomes a reliable indicator of phase transitions.
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Affiliation(s)
- Jia Bao
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Longhui Shen
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Hongying Liu
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Bin Guo
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Zhaoyu Sun
- School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023, People's Republic of China
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Gauthé O, Mila F. Thermal Ising Transition in the Spin-1/2 J_{1}-J_{2} Heisenberg Model. PHYSICAL REVIEW LETTERS 2022; 128:227202. [PMID: 35714253 DOI: 10.1103/physrevlett.128.227202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J_{1}-J_{2} Heisenberg model on the square lattice. In units of J_{2}, the critical temperature reaches a maximal value of T_{c}/J_{2}≃0.18 around J_{2}/J_{1}≃1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J_{2}/J_{1}≃0.6, and it vanishes as 1/log(J_{2}/J_{1}) in the large J_{2}/J_{1} limit, as predicted by Chandra et al., [Phys. Rev. Lett. 64, 88 (1990)PRLTAO0031-900710.1103/PhysRevLett.64.88]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.
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Affiliation(s)
- Olivier Gauthé
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Frédéric Mila
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Rau JG, McClarty PA, Moessner R. Pseudo-Goldstone Gaps and Order-by-Quantum Disorder in Frustrated Magnets. PHYSICAL REVIEW LETTERS 2018; 121:237201. [PMID: 30576168 DOI: 10.1103/physrevlett.121.237201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Indexed: 06/09/2023]
Abstract
In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as "order-by-quantum disorder," quantum zero-point fluctuations can lift the degeneracy and induce a gap for these modes. We show that this gap can be exactly computed at leading order in 1/S in spin-wave theory from the mean curvature of the classical and quantum zero-point energies-without the need to consider any spin-wave interactions. We confirm this equivalence through direct calculations of the spin-wave spectrum to O(1/S^{2}) in a wide variety of theoretically and experimentally relevant quantum spin models. We prove this equivalence through the use of an exact sum rule that provides the required mixing of different orders of 1/S. Finally, we discuss some implications for several leading order-by-quantum-disorder candidate materials, clarifying the expected pseudo-Goldstone gap sizes in Er_{2}Ti_{2}O_{7} and Ca_{3}Fe_{2}Ge_{3}O_{12}.
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Affiliation(s)
- Jeffrey G Rau
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Paul A McClarty
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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Mi BZ. Magnetism and thermodynamics of the anisotropic frustrated spin-1 Heisenberg antiferromagnet on a body-centered cubic lattice. SOLID STATE COMMUNICATIONS 2017; 251:79-87. [DOI: 10.1016/j.ssc.2016.12.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Rehn J, Sen A, Damle K, Moessner R. Classical Spin Liquid on the Maximally Frustrated Honeycomb Lattice. PHYSICAL REVIEW LETTERS 2016; 117:167201. [PMID: 27792369 DOI: 10.1103/physrevlett.117.167201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Indexed: 06/06/2023]
Abstract
We show that the honeycomb Heisenberg antiferromagnet with J_{1}/2=J_{2}=J_{3}, where J_{1}, J_{2}, and J_{3} are first-, second-, and third-neighbor couplings, respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with nonmagnetic ions, fractionalized degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low temperature is that of spins randomly located on a triangular lattice, with a frustrated sublattice-sensitive interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder. This comes with a clear experimental diagnostic in neutron scattering, which turns out to apply also to the case of the celebrated planar order by disorder of the kagome Heisenberg antiferromagnet.
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Affiliation(s)
- J Rehn
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Arnab Sen
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Kedar Damle
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India
| | - R Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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Mi BZ. Thermodynamic properties of frustrated arbitrary spin-S J1–J2 quantum Heisenberg antiferromagnet on the body-centered-cubic lattice in random phase approximation. SOLID STATE COMMUNICATIONS 2016; 239:20-26. [DOI: 10.1016/j.ssc.2016.04.015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Ren YZ, Tong NH, Xie XC. Cluster mean-field theory study of J1-J2 Heisenberg model on a square lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:115601. [PMID: 24589877 DOI: 10.1088/0953-8984/26/11/115601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries J(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.
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Affiliation(s)
- Yong-Zhi Ren
- Department of Physics, Renmin University of China, 100872 Beijing, People's Republic of China
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Rojas O, Hamer CJ, Oitmaa J. A frustrated three-dimensional antiferromagnet: stacked J1-J2 layers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:416001. [PMID: 21945890 DOI: 10.1088/0953-8984/23/41/416001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study a frustrated 3D antiferromagnet of stacked J(1)-J(2) layers. The intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this, there is a direct first-order transition from Néel to columnar order. Possible applications to real materials are discussed.
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Affiliation(s)
- Onofre Rojas
- School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
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Schmalfuss D, Darradi R, Richter J, Schulenburg J, Ihle D. Quantum J1-J2 antiferromagnet on a stacked square lattice: influence of the interlayer coupling on the ground-state magnetic ordering. PHYSICAL REVIEW LETTERS 2006; 97:157201. [PMID: 17155352 DOI: 10.1103/physrevlett.97.157201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2006] [Indexed: 05/12/2023]
Abstract
Using the coupled-cluster method and the rotation-invariant Green's function method, we study the influence of the interlayer coupling Jperpendicular on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (Jperpendicular=0), we find that the phases with magnetic long-range order at small J2<Jc1 and large J2>Jc2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling Jperpendicular >0, the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small Jperpendicular approximately (0.2-0.3)J1.
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Affiliation(s)
- D Schmalfuss
- Institut für Theoretische Physik, Universität Magdeburg, 39016 Magdeburg, Germany
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Capriotti L, Fubini A, Roscilde T, Tognetti V. Ising transition in the two-dimensional quantum J1-J2 Heisenberg model. PHYSICAL REVIEW LETTERS 2004; 92:157202. [PMID: 15169314 DOI: 10.1103/physrevlett.92.157202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2003] [Indexed: 05/24/2023]
Abstract
We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings in its collinear phase (J(2)/J(1)>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J(2)/J(1) is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin and temperature dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li2VOSiO4 and related compounds.
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Affiliation(s)
- Luca Capriotti
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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Weber C, Capriotti L, Misguich G, Becca F, Elhajal M, Mila F. Ising transition driven by frustration in a 2D classical model with continuous symmetry. PHYSICAL REVIEW LETTERS 2003; 91:177202. [PMID: 14611373 DOI: 10.1103/physrevlett.91.177202] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2003] [Indexed: 05/24/2023]
Abstract
We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J1) and next-nearest (J2) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J2/J1>1/2, thermal fluctuations give rise to an effective Z2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T(c)-->0 with an infinite slope when J2/J1-->1/2.
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Affiliation(s)
- Cédric Weber
- Institut de Physique Théorique, Université de Lausanne, CH-1015 Lausanne, Switzerland
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