1
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Li H, Lv E, Xi N, Gao Y, Qi Y, Li W, Su G. Magnetocaloric effect of topological excitations in Kitaev magnets. Nat Commun 2024; 15:7011. [PMID: 39147763 PMCID: PMC11327298 DOI: 10.1038/s41467-024-51146-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 07/29/2024] [Indexed: 08/17/2024] Open
Abstract
Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.
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Affiliation(s)
- Han Li
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Enze Lv
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Ning Xi
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Yuan Gao
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Peng Huanwu Collaborative Center for Research and Education, and School of Physics, Beihang University, Beijing, 100191, China
| | - Yang Qi
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, 200433, China
| | - Wei Li
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Peng Huanwu Collaborative Center for Research and Education, and School of Physics, Beihang University, Beijing, 100191, China.
| | - Gang Su
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
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2
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Das J, Kundu S, Kumar A, Tripathi V. Field tuning Kitaev systems for spin fractionalization and topological order. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:443001. [PMID: 39059430 DOI: 10.1088/1361-648x/ad6827] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Accepted: 07/26/2024] [Indexed: 07/28/2024]
Abstract
The honeycomb Kitaev model describes aZ2spin liquid with topological order and fractionalized excitations consisting of gappedπ-fluxes and free Majorana fermions. Competing interactions, even when not very strong, are known to destabilize the Kitaev spin liquid. Magnetic fields are a convenient parameter for tuning between different phases of the Kitaev systems, and have even been investigated for potentially counteracting the effects of other destabilizing interactions leading to a revival of the topological phase. Here we review the progress in understanding the effects of magnetic fields on some of the perturbed Kitaev systems, particularly on fractionalization and topological order.
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Affiliation(s)
- J Das
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai, India
| | - S Kundu
- Department of Physics, University of Florida, Gainesville, FL 32611, United States of America
| | - A Kumar
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, United States of America
| | - V Tripathi
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai, India
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3
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Sur S, Xu Y, Li S, Gong SS, Nevidomskyy AH. Field-Induced Non-BEC Transitions in Frustrated Magnets. PHYSICAL REVIEW LETTERS 2024; 132:066701. [PMID: 38394558 DOI: 10.1103/physrevlett.132.066701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Revised: 12/12/2023] [Accepted: 01/04/2024] [Indexed: 02/25/2024]
Abstract
Frustrated spin systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic J_{1}-J_{2}-J_{3} model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the Néel order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the Néel phase from other magnetically ordered states.
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Affiliation(s)
- Shouvik Sur
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Yi Xu
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Shuyi Li
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Shou-Shu Gong
- School of Physical Sciences, Great Bay University, Dongguan 523000, China, and Great Bay Institute for Advanced Study, Dongguan 523000, China
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4
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Zhang X, Xu Y, Halloran T, Zhong R, Broholm C, Cava RJ, Drichko N, Armitage NP. A magnetic continuum in the cobalt-based honeycomb magnet BaCo 2(AsO 4) 2. NATURE MATERIALS 2023; 22:58-63. [PMID: 36411349 DOI: 10.1038/s41563-022-01403-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 10/10/2022] [Indexed: 06/16/2023]
Abstract
Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.
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Affiliation(s)
- Xinshu Zhang
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA
| | - Yuanyuan Xu
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA
| | - T Halloran
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA
| | - Ruidan Zhong
- Department of Chemistry, Princeton University, Princeton, NJ, USA
| | - C Broholm
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - R J Cava
- Department of Chemistry, Princeton University, Princeton, NJ, USA
| | - N Drichko
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA
| | - N P Armitage
- Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA.
- Canadian Institute for Advanced Research, Toronto, Ontario, Canada.
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5
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Yang B, Goh YM, Sung SH, Ye G, Biswas S, Kaib DAS, Dhakal R, Yan S, Li C, Jiang S, Chen F, Lei H, He R, Valentí R, Winter SM, Hovden R, Tsen AW. Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl 3. NATURE MATERIALS 2023; 22:50-57. [PMID: 36396963 DOI: 10.1038/s41563-022-01401-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 10/07/2022] [Indexed: 06/16/2023]
Abstract
Layered α-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl3, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit.
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Affiliation(s)
- Bowen Yang
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada
| | - Yin Min Goh
- Department of Physics, University of Michigan, Ann Arbor, MI, USA
| | - Suk Hyun Sung
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Gaihua Ye
- Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX, USA
| | - Sananda Biswas
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany
| | - David A S Kaib
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany
| | - Ramesh Dhakal
- Department of Physics and Center for Functional Materials, Wake Forest University, Winston-Salem, NC, USA
| | - Shaohua Yan
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, China
| | - Chenghe Li
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, China
| | - Shengwei Jiang
- Department of Physics, Cornell University, Ithaca, NY, USA
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Fangchu Chen
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada
| | - Hechang Lei
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, China
| | - Rui He
- Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX, USA
| | - Roser Valentí
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany
| | - Stephen M Winter
- Department of Physics and Center for Functional Materials, Wake Forest University, Winston-Salem, NC, USA.
| | - Robert Hovden
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA.
- Applied Physics Program, University of Michigan, Ann Arbor, MI, USA.
| | - Adam W Tsen
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada.
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada.
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6
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Abstract
AbstractRecent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.
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7
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Identification of a Kitaev quantum spin liquid by magnetic field angle dependence. Nat Commun 2022; 13:323. [PMID: 35031621 PMCID: PMC8760334 DOI: 10.1038/s41467-021-27943-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 12/28/2021] [Indexed: 12/03/2022] Open
Abstract
Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments. Non-Abelian phase of Kitaev quantum spin liquid is promising for topological quantum computation. Here, the authors propose a way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence, providing criteria for such a state for future experiments.
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8
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Li H, Zhang HK, Wang J, Wu HQ, Gao Y, Qu DW, Liu ZX, Gong SS, Li W. Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl 3. Nat Commun 2021; 12:4007. [PMID: 34188044 PMCID: PMC8242101 DOI: 10.1038/s41467-021-24257-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/07/2021] [Indexed: 11/15/2022] Open
Abstract
The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.
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Affiliation(s)
- Han Li
- School of Physics, Beihang University, Beijing, China
| | - Hao-Kai Zhang
- School of Physics, Beihang University, Beijing, China
- Institute for Advanced Study, Tsinghua University, Beijing, China
| | - Jiucai Wang
- Institute for Advanced Study, Tsinghua University, Beijing, China
- Department of Physics, Renmin University of China, Beijing, China
| | - Han-Qing Wu
- Center for Neutron Science and Technology, School of Physics, Sun Yat-sen University, Guangzhou, China
| | - Yuan Gao
- School of Physics, Beihang University, Beijing, China
| | - Dai-Wei Qu
- School of Physics, Beihang University, Beijing, China
| | - Zheng-Xin Liu
- Department of Physics, Renmin University of China, Beijing, China.
| | - Shou-Shu Gong
- School of Physics, Beihang University, Beijing, China.
- International Research Institute of Multidisciplinary Science, Beihang University, Beijing, China.
| | - Wei Li
- School of Physics, Beihang University, Beijing, China.
- International Research Institute of Multidisciplinary Science, Beihang University, Beijing, China.
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
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9
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Jiang MH, Liang S, Chen W, Qi Y, Li JX, Wang QH. Tuning Topological Orders by a Conical Magnetic Field in the Kitaev Model. PHYSICAL REVIEW LETTERS 2020; 125:177203. [PMID: 33156649 DOI: 10.1103/physrevlett.125.177203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 06/25/2019] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
We show that a conical magnetic field H=(1,1,1)H can be used to tune the topological order and hence, anyon excitations of the Z_{2} quantum spin liquid in the isotropic antiferromagnetic Kitaev model. A novel topological order, featured with Chern number C=4 and Abelian anyon excitations, is induced in a narrow range of intermediate fields H_{c1}≤H≤H_{c2}. On the other hand, the C=1 Ising-topological order with non-Abelian anyon excitations, as previously known to be present at small fields, is found here to survive up to H_{c1}. The results are obtained by developing and applying a Z_{2} mean field theory that works at finite fields and is asymptotically exact in the zero field limit and the associated variational quantum Monte Carlo.
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Affiliation(s)
- Ming-Hong Jiang
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
| | - Shuang Liang
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
| | - Wei Chen
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Yang Qi
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
- State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - Jian-Xin Li
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Qiang-Hua Wang
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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10
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Keselman A, Bauer B, Xu C, Jian CM. Emergent Fermi Surface in a Triangular-Lattice SU(4) Quantum Antiferromagnet. PHYSICAL REVIEW LETTERS 2020; 125:117202. [PMID: 32976015 DOI: 10.1103/physrevlett.125.117202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Revised: 06/18/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group method, which we support with a field theory analysis.
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Affiliation(s)
- Anna Keselman
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - Bela Bauer
- Microsoft Station Q, Santa Barbara, California 93106-6105, USA
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Chao-Ming Jian
- Microsoft Station Q, Santa Barbara, California 93106-6105, USA
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11
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Minakawa T, Murakami Y, Koga A, Nasu J. Majorana-Mediated Spin Transport in Kitaev Quantum Spin Liquids. PHYSICAL REVIEW LETTERS 2020; 125:047204. [PMID: 32794825 DOI: 10.1103/physrevlett.125.047204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with zigzag edges using the time-dependent Majorana mean-field theory. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the S=1/2 spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system despite the presence of a nonzero spin gap. We also demonstrate that this phenomenon can be observed in the system with small Heisenberg interactions using the exact diagonalization.
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Affiliation(s)
- Tetsuya Minakawa
- Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152- 8551, Japan
| | - Yuta Murakami
- Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152- 8551, Japan
| | - Akihisa Koga
- Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152- 8551, Japan
| | - Joji Nasu
- Department of Physics, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan
- PRESTO, Japan Science and Technology Agency, Honcho Kawaguchi, Saitama 332-0012, Japan
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12
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Hu WJ, Zhang Y, Nevidomskyy AH, Dagotto E, Si Q, Lai HH. Fractionalized Excitations Revealed by Entanglement Entropy. PHYSICAL REVIEW LETTERS 2020; 124:237201. [PMID: 32603177 DOI: 10.1103/physrevlett.124.237201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 05/27/2020] [Indexed: 06/11/2023]
Abstract
Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.
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Affiliation(s)
- Wen-Jun Hu
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Yi Zhang
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
| | - Andriy H Nevidomskyy
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Elbio Dagotto
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Qimiao Si
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Hsin-Hua Lai
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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13
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Zhong R, Gao T, Ong NP, Cava RJ. Weak-field induced nonmagnetic state in a Co-based honeycomb. SCIENCE ADVANCES 2020; 6:eaay6953. [PMID: 32042902 PMCID: PMC6981077 DOI: 10.1126/sciadv.aay6953] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Accepted: 11/21/2019] [Indexed: 06/10/2023]
Abstract
Layered honeycomb magnets are of interest as potential realizations of the Kitaev quantum spin liquid (KQSL), a quantum state with long-range spin entanglement and an exactly solvable Hamiltonian. Conventional magnetically ordered states are present for all currently known candidate materials, however, because non-Kitaev terms in the Hamiltonians obscure the Kitaev physics. Current experimental studies of the KQSL are focused on 4d or 5d transition metal-based honeycombs, in which strong spin-orbit coupling can be expected, yielding Kitaev interaction that dominates in an applied magnetic field. In contrast, for 3d-based layered honeycomb magnets, spin-orbit coupling is weak, and thus, Kitaev physics should be substantially less accessible. Here, we report our studies on BaCo2(AsO4)2, for which we find that the magnetic order associated with the non-Kitaev interactions can be fully suppressed by a relatively low magnetic field, yielding a nonmagnetic material and implying the presence of strong magnetic frustration and weak non-Kitaev interactions.
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Affiliation(s)
- Ruidan Zhong
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
| | - Tong Gao
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Nai Phuan Ong
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Robert J. Cava
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
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14
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Stavropoulos PP, Pereira D, Kee HY. Microscopic Mechanism for a Higher-Spin Kitaev Model. PHYSICAL REVIEW LETTERS 2019; 123:037203. [PMID: 31386455 DOI: 10.1103/physrevlett.123.037203] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 06/10/2023]
Abstract
The spin S=1/2 Kitaev honeycomb model has attracted significant attention since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions and strong Hund's coupling in transition metal cations. The S=1 Kitaev and ferromagnetic Heisenberg interactions are generated from superexchange paths. Taking into account the antiferromagnetic Heisenberg term from direct-exchange paths, the Kitaev interaction dominates the physics of the S=1 system. Using an exact diagonalization technique, we show a finite regime of S=1 spin liquid in the presence of the Heisenberg interaction. Candidate materials are proposed, and generalization to higher spins is discussed.
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Affiliation(s)
- P Peter Stavropoulos
- Department of Physics and Center for Quantum Materials, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada
| | - D Pereira
- Department of Physics and Center for Quantum Materials, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada
| | - Hae-Young Kee
- Department of Physics and Center for Quantum Materials, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8, Canada
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15
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Abstract
Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid-the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl3. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.
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