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Rousochatzakis I, Perkins NB, Luo Q, Kee HY. Beyond Kitaev physics in strong spin-orbit coupled magnets. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:026502. [PMID: 38241723 DOI: 10.1088/1361-6633/ad208d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 01/19/2024] [Indexed: 01/21/2024]
Abstract
We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.
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Affiliation(s)
| | - Natalia B Perkins
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, United States of America
- Technical University of Munich, Munich, Germany
- Institute for Advanced Study, D-85748 Garching, Germany
| | - Qiang Luo
- College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People's Republic of China
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Hae-Young Kee
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
- Canadian Institute for Advanced Research, CIFAR Program in Quantum Materials, Toronto, Ontario M5G 1M1, Canada
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2
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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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3
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Zhang Y, Zhao Y, Chen L, Pan X, Xu M, Li Z, Zhou Y, Wu Y. Locating fixed points in the phase plane. Phys Rev E 2019; 100:052146. [PMID: 31870026 DOI: 10.1103/physreve.100.052146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Indexed: 06/10/2023]
Abstract
The critical point is a fixed point in finite-size scaling. To quantify the behavior of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of the fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of the fixed point, which can be a critical point, a point of the first-order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the three-dimensional three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the Beam Energy Scan program of the Relativistic Heavy Ion Collider.
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Affiliation(s)
- Yanhua Zhang
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Yeyin Zhao
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Lizhu Chen
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
| | - Xue Pan
- School of Electronic Engineering, Chengdu Technological University, Chengdu 611730, China
| | - Mingmei Xu
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Zhiming Li
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Yu Zhou
- No.1 Middle School Affiliated to Central China Normal University, Wuhan 430223, China
| | - Yuanfang Wu
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
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Schecter M, Syljuåsen OF, Paaske J. Nematic Bond Theory of Heisenberg Helimagnets. PHYSICAL REVIEW LETTERS 2017; 119:157202. [PMID: 29077464 DOI: 10.1103/physrevlett.119.157202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Indexed: 06/07/2023]
Abstract
We study classical two-dimensional frustrated Heisenberg models with generically incommensurate ground states. A new theory for the lattice-nematic "order by disorder" transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wave vector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.
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Affiliation(s)
- Michael Schecter
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Olav F Syljuåsen
- Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
| | - Jens Paaske
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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5
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Adolphs CPJ, Moser S, Sawatzky GA, Berciu M. Non-Zhang-Rice Singlet Character of the First Ionization State of T-CuO. PHYSICAL REVIEW LETTERS 2016; 116:087002. [PMID: 26967437 DOI: 10.1103/physrevlett.116.087002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2015] [Indexed: 06/05/2023]
Abstract
We argue that tetragonal CuO (T-CuO) has the potential to finally settle long-standing modeling issues for cuprate physics. We compare the one-hole quasiparticle (qp) dispersion of T-CuO to that of cuprates, in the framework of the strongly correlated (U_{dd}→∞) limit of the three-band Emery model. Unlike in CuO_{2}, magnetic frustration in T-CuO breaks the C_{4} rotational symmetry and leads to strong deviations from the Zhang-Rice singlet picture in parts of the reciprocal space. Our results are consistent with angle-resolved photoemission spectroscopy data but in sharp contradiction to those of a one-band model previously suggested for them. These differences identify T-CuO as an ideal material to test a variety of scenarios proposed for explaining cuprate phenomenology.
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Affiliation(s)
- Clemens P J Adolphs
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z1
| | - Simon Moser
- Institute of Condensed Matter Physics, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland
- Advanced Light Source, Berkeley, California 94720, USA
| | - George A Sawatzky
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z1
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z4
| | - Mona Berciu
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z1
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z4
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Nishimoto S, Katukuri VM, Yushankhai V, Stoll H, Rößler UK, Hozoi L, Rousochatzakis I, van den Brink J. Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3. Nat Commun 2016; 7:10273. [PMID: 26776664 PMCID: PMC4735606 DOI: 10.1038/ncomms10273] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Accepted: 11/24/2015] [Indexed: 11/09/2022] Open
Abstract
Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.
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Affiliation(s)
- Satoshi Nishimoto
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Vamshi M Katukuri
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Viktor Yushankhai
- Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Russia.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Street 38, 01187 Dresden, Germany
| | - Hermann Stoll
- Institute for Theoretical Chemistry, Universität Stuttgart, Pfaffenwaldring 55, 70550 Stuttgart, Germany
| | - Ulrich K Rößler
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Liviu Hozoi
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Ioannis Rousochatzakis
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Street 38, 01187 Dresden, Germany
| | - Jeroen van den Brink
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany.,Department of Physics, Technical University Dresden, Helmholtzstrasse 10, 01069 Dresden, Germany
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7
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Jeevanesan B, Chandra P, Coleman P, Orth PP. Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment. PHYSICAL REVIEW LETTERS 2015; 115:177201. [PMID: 26551137 DOI: 10.1103/physrevlett.115.177201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Indexed: 06/05/2023]
Abstract
In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z(6) order.
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Affiliation(s)
- Bhilahari Jeevanesan
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Premala Chandra
- Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Piers Coleman
- Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
- Hubbard Theory Consortium and Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Peter P Orth
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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8
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Starykh OA. Unusual ordered phases of highly frustrated magnets: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:052502. [PMID: 25892088 DOI: 10.1088/0034-4885/78/5/052502] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with S(z) = ± 1. We discuss extensively the R - h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S = 1/2 limit. When possible, we point out connections with experimental findings.
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Affiliation(s)
- Oleg A Starykh
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112-0830, USA
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9
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Moser S, Moreschini L, Yang HY, Innocenti D, Fuchs F, Hansen NH, Chang YJ, Kim KS, Walter AL, Bostwick A, Rotenberg E, Mila F, Grioni M. Angle-resolved photoemission spectroscopy of tetragonal CuO: evidence for intralayer coupling between cupratelike sublattices. PHYSICAL REVIEW LETTERS 2014; 113:187001. [PMID: 25396389 DOI: 10.1103/physrevlett.113.187001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Indexed: 06/04/2023]
Abstract
We investigate by angle-resolved photoemission the electronic structure of in situ grown tetragonal CuO, a synthetic quasi-two-dimensional edge-sharing cuprate. We show that, in spite of the very different nature of the copper oxide layers, with twice as many Cu in the CuO layers of tetragonal CuO as compared to the CuO(2) layers of the high-T(c) cuprates, the low-energy electronic excitations are surprisingly similar, with a Zhang-Rice singlet dispersing on weakly coupled cupratelike sublattices. This system should thus be considered as a member of the high-T(c) cuprate family, with, however, interesting differences due to the intralayer coupling between the cupratelike sublattices.
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Affiliation(s)
- S Moser
- Institute of Condensed Matter Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and Advanced Light Source (ALS), Berkeley, California 94720, USA
| | - L Moreschini
- Advanced Light Source (ALS), Berkeley, California 94720, USA
| | - H-Y Yang
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - D Innocenti
- Advanced Light Source (ALS), Berkeley, California 94720, USA and Dipartimento di Ingegneria Meccanica, Università di Roma Tor Vergata, I-00133 Roma, Italy
| | - F Fuchs
- Experimental Physics VI, Julius-Maximilian University of Würzburg, 97074 Würzburg, Germany
| | - N H Hansen
- Experimental Physics VI, Julius-Maximilian University of Würzburg, 97074 Würzburg, Germany and ZAE Bayern, Am Hubland, 97074 Würzburg, Germany
| | - Y J Chang
- Advanced Light Source (ALS), Berkeley, California 94720, USA and Department of Physics, University of Seoul, Seoul 130-743, Korea
| | - K S Kim
- Advanced Light Source (ALS), Berkeley, California 94720, USA and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea and Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang 790-784, Korea
| | - A L Walter
- Advanced Light Source (ALS), Berkeley, California 94720, USA and Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - A Bostwick
- Advanced Light Source (ALS), Berkeley, California 94720, USA
| | - E Rotenberg
- Advanced Light Source (ALS), Berkeley, California 94720, USA
| | - F Mila
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - M Grioni
- Institute of Condensed Matter Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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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: 2] [Impact Index Per Article: 0.2] [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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11
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Tamura R, Tanaka S. Interlayer-interaction dependence of latent heat in the Heisenberg model on a stacked triangular lattice with competing interactions. Phys Rev E 2013; 88:052138. [PMID: 24329245 DOI: 10.1103/physreve.88.052138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2013] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- Ryo Tamura
- International Center for Young Scientists, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba-shi, Ibaraki 305-0047, Japan
| | - Shu Tanaka
- Department of Chemistry, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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12
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Mezio A, Sposetti CN, Manuel LO, Trumper AE. Broken discrete and continuous symmetries in two-dimensional spiral antiferromagnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:465602. [PMID: 24153423 DOI: 10.1088/0953-8984/25/46/465602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We study the occurrence of symmetry breaking, at zero and finite temperatures, in the J1-J3 antiferromagnetic Heisenberg model on the square lattice using Schwinger boson mean field theory. For spin-1/2 the ground state always breaks the SU(2) symmetry with a continuous quasi-critical transition at J3/J1 ∼ 0.38, from Néel to spiral long range order, although local spin fluctuation considerations suggest an intermediate disordered regime around 0.35 ≲ J3/J1 ≲ 0.5, in qualitative agreement with recent numerical results. At low temperatures we find a Z2 broken symmetry region with short range spiral order characterized by an Ising-like nematic order parameter that compares qualitatively well with classical Monte Carlo results. At intermediate temperatures the phase diagram shows regions with collinear short range orders: for J3/J1 < 1 Néel (π,π) correlations and for J3/J1 > 1 a novel phase consisting of four decoupled third neighbour sublattices with Néel (π,π) correlations in each one. We conclude that the effect of quantum and thermal fluctuations is to favour collinear correlations even in the strongly frustrated regime.
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Affiliation(s)
- A Mezio
- Instituto de Física Rosario (CONICET) and Universidad Nacional de Rosario, Boulevard 27 de Febrero 210 bis, (2000) Rosario, Argentina
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13
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Tanaka H. Importance of many-body orientational correlations in the physical description of liquids. Faraday Discuss 2013; 167:9-76. [DOI: 10.1039/c3fd00110e] [Citation(s) in RCA: 71] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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14
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Orth PP, Chandra P, Coleman P, Schmalian J. Emergent critical phase and Ricci flow in a 2D frustrated Heisenberg model. PHYSICAL REVIEW LETTERS 2012; 109:237205. [PMID: 23368258 DOI: 10.1103/physrevlett.109.237205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Indexed: 06/01/2023]
Abstract
We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we obtain the scaling of the spin stiffnesses governed by the Ricci flow of a four-dimensional metric tensor. At low temperatures, the relative phase between the spins on the two sublattices is described by a six-state clock model with an emergent critical phase.
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Affiliation(s)
- Peter P Orth
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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15
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Tanaka H. Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:113. [PMID: 23104614 DOI: 10.1140/epje/i2012-12113-y] [Citation(s) in RCA: 176] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2012] [Accepted: 09/28/2012] [Indexed: 06/01/2023]
Abstract
There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.
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Affiliation(s)
- Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, 153-8505, Tokyo, Japan.
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16
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Tanaka H. Roles of bond orientational ordering in glass transition and crystallization. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:284115. [PMID: 21709320 DOI: 10.1088/0953-8984/23/28/284115] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid-solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.
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Affiliation(s)
- Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Tokyo, Japan.
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17
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Gvozdikova MV, Melchy PE, Zhitomirsky ME. Magnetic phase diagrams of classical triangular and kagome antiferromagnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:164209. [PMID: 21471626 DOI: 10.1088/0953-8984/23/16/164209] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the effect of geometrical frustration on the H-T phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large-scale Monte Carlo simulations. For the kagome antiferromagnet, thermal fluctuations are unable to lift degeneracy completely and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagome antiferromagnet. In the low-field regime, the Kosterlitz-Thouless transition into a spin-nematic phase is produced by unbinding of half-quantum vortices.
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Affiliation(s)
- M V Gvozdikova
- Department of Physics, Kharkov National University, 61077 Kharkov, Ukraine
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18
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Tanaka H, Kawasaki T, Shintani H, Watanabe K. Critical-like behaviour of glass-forming liquids. NATURE MATERIALS 2010; 9:324-331. [PMID: 20173749 DOI: 10.1038/nmat2634] [Citation(s) in RCA: 160] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2009] [Accepted: 01/13/2010] [Indexed: 05/28/2023]
Abstract
Recently it has been revealed that when approaching the glass-transition temperature, T(g), the dynamics of a liquid not only drastically slows down, but also becomes progressively more heterogeneous. From our simulations and experiments of six different glass-forming liquids, we find that the heterogeneous dynamics is a result of critical-like fluctuations of static structural order, contrary to a common belief that it is purely of dynamic origin. The static correlation length and susceptibility of a structural order parameter show Ising-like power-law divergence towards the ideal glass-transition point. However, this structural ordering accompanies little density change, which explains why it has not been detected by the static structure factor so far. Our results suggest a far more direct link than thought before between glass transition and critical phenomena. Indeed, the glass transition may be a new type of critical phenomenon where a structural order parameter is directly linked to slowness.
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Affiliation(s)
- Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
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19
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Capriotti L, Sachdev S. Low-temperature broken-symmetry phases of spiral antiferromagnets. PHYSICAL REVIEW LETTERS 2004; 93:257206. [PMID: 15697936 DOI: 10.1103/physrevlett.93.257206] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2004] [Indexed: 05/24/2023]
Abstract
We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of spin S-->infinity, there is a zero temperature (T) Lifshitz point at J(3)=1/4J(1), with long-range spiral spin order at T=0 for J3>1/4J(1). We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0< or =T<T(c) approximately (J3-1/4J(1))S2. The transition at T=T(c) is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.
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Affiliation(s)
- Luca Capriotti
- Valuation Risk Group, Credit Suisse First Boston (Europe) Ltd., One Cabot Square, London E14 4QJ, UK
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20
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Schmid G, Troyer M. Melting of bosonic stripes. PHYSICAL REVIEW LETTERS 2004; 93:067003. [PMID: 15323656 DOI: 10.1103/physrevlett.93.067003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2003] [Indexed: 05/24/2023]
Abstract
We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
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Affiliation(s)
- Guido Schmid
- Theoretische Physik, Eidgenössische Technische Hochschule Zürich, CH-8093, Switzerland
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21
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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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