1
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Liu YK, Cao PC, Qi M, Huang QKL, Gao F, Peng YG, Li Y, Zhu XF. Observation of non-Hermitian skin effect in thermal diffusion. Sci Bull (Beijing) 2024; 69:1228-1236. [PMID: 38503653 DOI: 10.1016/j.scib.2024.02.040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2023] [Revised: 02/01/2024] [Accepted: 02/26/2024] [Indexed: 03/21/2024]
Abstract
The paradigm shift of Hermitian systems into the non-Hermitian regime profoundly modifies inherent property of the topological systems, leading to various unprecedented effects such as the non-Hermitian skin effect (NHSE). In the past decade, the NHSE has been demonstrated in quantum, optical and acoustic systems. Beside those wave systems, the NHSE in diffusive systems has not yet been observed, despite recent abundant advances in the study of topological thermal diffusion. In this work, we design a thermal diffusion lattice based on a modified Su-Schrieffer-Heeger model and demonstrate the diffusive NHSE. In the proposed model, the asymmetric temperature field coupling inside each unit cell can be judiciously realized by appropriate configurations of structural parameters. We find that the temperature fields trend to concentrate toward the target boundary which is robust against initial excitation conditions. We thus experimentally demonstrated the NHSE in thermal diffusion and verified its robustness against various defects. Our work provides a platform for exploration of non-Hermitian physics in the diffusive systems, which has important applications in efficient heat collection, highly sensitive thermal sensing and others.
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Affiliation(s)
- Yun-Kai Liu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Pei-Chao Cao
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Minghong Qi
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Qiang-Kai-Lai Huang
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Feng Gao
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yu-Gui Peng
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China.
| | - Ying Li
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China.
| | - Xue-Feng Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China.
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2
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Yu XJ, Pan Z, Xu L, Li ZX. Non-Hermitian Strongly Interacting Dirac Fermions. PHYSICAL REVIEW LETTERS 2024; 132:116503. [PMID: 38563924 DOI: 10.1103/physrevlett.132.116503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 12/22/2023] [Accepted: 02/27/2024] [Indexed: 04/04/2024]
Abstract
Exotic quantum phases and phase transition in the strongly interacting Dirac systems have attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment, emerges as a frontier of modern physics in recent years. In this Letter, we investigate the interplay between non-Hermitian physics and strong correlation in Dirac-fermion systems. We generalize the projector quantum Monte-Carlo (PQMC) algorithm to the non-Hermitian interacting fermionic systems. Employing PQMC simulation, we decipher the ground-state phase diagram of the honeycomb Hubbard model with spin resolved non-Hermitian asymmetric hopping processes. The antiferromagnetic (AFM) ordering induced by Hubbard interaction is enhanced by the non-Hermitian asymmetric hopping. Combining PQMC simulation and renormalization group analysis, we reveal that the quantum phase transition between Dirac semi-metal and AFM phases belongs to Hermitian chiral XY universality class, implying that a Hermitian Gross-Neveu transition is emergent at the quantum critical point although the model is non-Hermitian.
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Affiliation(s)
- Xue-Jia Yu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Zhiming Pan
- Department of Physics, School of Science, Westlake University, Hangzhou 310030, China
- Institute for Theoretical Sciences, Westlake University, Hangzhou 310024, China
| | - Limei Xu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing 100871, China
| | - Zi-Xiang Li
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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3
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Zhang XX, Nagaosa N. Topological spin textures in electronic non-Hermitian systems. Sci Bull (Beijing) 2024; 69:325-333. [PMID: 38129237 DOI: 10.1016/j.scib.2023.12.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Revised: 08/17/2023] [Accepted: 11/29/2023] [Indexed: 12/23/2023]
Abstract
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification of observables. However, their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired, where a variety of materials are available, calculations are solidly founded, and accurate spectroscopic techniques can be applied. We demonstrate that, in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities, highly nontrivial topological soliton spin textures appear in momentum space. Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically. Moreover, the distinct topological soliton objects can be deformed to each other, mediated by topological transitions driven by tuning across a critical direction of doped magnetism. These results not only open a solid-state avenue to exotic spin patterns via spin- and angle-resolved photoemission spectroscopy, but also inspire non-Hermitian dissipation engineering of spins in solids.
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Affiliation(s)
- Xiao-Xiao Zhang
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.
| | - Naoto Nagaosa
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan; Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan.
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4
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Sayyad S, Lado JL. Transfer learning from Hermitian to non-Hermitian quantum many-body physics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:185603. [PMID: 38277690 DOI: 10.1088/1361-648x/ad22f8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 01/26/2024] [Indexed: 01/28/2024]
Abstract
Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.
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Affiliation(s)
- Sharareh Sayyad
- Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Jose L Lado
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Espoo, Finland
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5
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Ouyang XY, Ye QJ, Li XZ. Complex phase diagram and supercritical matter. Phys Rev E 2024; 109:024118. [PMID: 38491632 DOI: 10.1103/physreve.109.024118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 01/11/2024] [Indexed: 03/18/2024]
Abstract
The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.
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Affiliation(s)
- Xiao-Yu Ouyang
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Qi-Jun Ye
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Xin-Zheng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, People's Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, People's Republic of China
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6
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Meden V, Grunwald L, Kennes DM. PT-symmetric, non-Hermitian quantum many-body physics-a methodological perspective. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:124501. [PMID: 37871599 DOI: 10.1088/1361-6633/ad05f3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 10/23/2023] [Indexed: 10/25/2023]
Abstract
We review the methodology to theoretically treat parity-time- (PT-) symmetric, non-Hermitian quantum many-body systems. They are realized as open quantum systems withPTsymmetry and couplings to the environment which are compatible.PT-symmetric non-Hermitian quantum systems show a variety of fascinating properties which single them out among generic open systems. The study of the latter has a long history in quantum theory. These studies are based on the Hermiticity of the combined system-reservoir setup and were developed by the atomic, molecular, and optical physics as well as the condensed matter physics communities. The interest of the mathematical physics community inPT-symmetric, non-Hermitian systems led to a new perspective and the development of the elegant mathematical formalisms ofPT-symmetric and biorthogonal quantum mechanics, which do not make any reference to the environment. In the mathematical physics research, the focus is mainly on the remarkable spectral properties of the Hamiltonians and the characteristics of the corresponding single-particle eigenstates. Despite being non-Hermitian, the Hamiltonians can show parameter regimes, in which all eigenvalues are real. To investigate emergent quantum many-body phenomena in condensed matter physics and to make contact to experiments one, however, needs to study expectation values of observables and correlation functions. One furthermore, has to investigate statistical ensembles and not only eigenstates. The adoption of the concepts ofPT-symmetric and biorthogonal quantum mechanics by parts of the condensed matter community led to a controversial status of the methodology. There is no consensus on fundamental issues, such as, what a proper observable is, how expectation values are supposed to be computed, and what adequate equilibrium statistical ensembles and their corresponding density matrices are. With the technological progress in engineering and controlling open quantum many-body systems it is high time to reconcile the Hermitian with thePT-symmetric and biorthogonal perspectives. We comprehensively review the different approaches, including the overreaching idea of pseudo-Hermiticity. To motivate the Hermitian perspective, which we propagate here, we mainly focus on the ancilla approach. It allows to embed a non-Hermitian system into a larger, Hermitian one. In contrast to other techniques, e.g. master equations, it does not rely on any approximations. We discuss the peculiarities ofPT-symmetric and biorthogonal quantum mechanics. In these, what is considered to be an observable depends on the Hamiltonian or the selected (biorthonormal) basis. Crucially in addition, what is denoted as an 'expectation value' lacks a direct probabilistic interpretation, and what is viewed as the canonical density matrix is non-stationary and non-Hermitian. Furthermore, the non-unitarity of the time evolution is hidden within the formalism. We pick up several model Hamiltonians, which so far were either investigated from the Hermitian perspective or from thePT-symmetric and biorthogonal one, and study them within the respective alternative framework. This includes a simple two-level, single-particle problem but also a many-body lattice model showing quantum critical behavior. Comparing the outcome of the two types of computations shows that the Hermitian approach, which, admittedly, is in parts clumsy, always leads to results which are physically sensible. In the rare cases, in which a comparison to experimental data is possible, they furthermore agree to these. In contrast, the mathematically elegantPT-symmetric and biorthogonal approaches lead to results which, are partly difficult to interpret physically. We thus conclude that the Hermitian methodology should be employed. However, to fully appreciate the physics ofPT-symmetric, non-Hermitian quantum many-body systems, it is also important to be aware of the main concepts ofPT-symmetric and biorthogonal quantum mechanics. Our conclusion has far reaching consequences for the application of Green function methods, functional integrals, and generating functionals, which are at the heart of a large number of many-body methods. They cannot be transferred in their established forms to treatPT-symmetric, non-Hermitian quantum systems. It can be considered as an irony of fate that these methods are available only within the mathematical formalisms ofPT-symmetric and biorthogonal quantum mechanics.
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Affiliation(s)
- V Meden
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany
| | - L Grunwald
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
| | - D M Kennes
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
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7
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Saha M, Agarwalla BK, Kulkarni M, Purkayastha A. Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points. PHYSICAL REVIEW LETTERS 2023; 130:187101. [PMID: 37204882 DOI: 10.1103/physrevlett.130.187101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 11/11/2022] [Accepted: 03/31/2023] [Indexed: 05/21/2023]
Abstract
We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.
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Affiliation(s)
- Madhumita Saha
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Ward No. 8, NCL Colony, Pashan, Pune, Maharashtra 411008, India
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Ward No. 8, NCL Colony, Pashan, Pune, Maharashtra 411008, India
| | - Manas Kulkarni
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Archak Purkayastha
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
- Department of Physics, Indian Institute of Technology, Hyderabad 502284, India
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8
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Cayao J. Exceptional degeneracies in non-Hermitian Rashba semiconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:254002. [PMID: 37021876 DOI: 10.1088/1361-648x/acc7e9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Abstract
Exceptional points (EPs) are spectral degeneracies of non-Hermitian (NH) systems where eigenvalues and eigenvectors coalesce, inducing unique topological phases that have no counterpart in the Hermitian realm. Here we consider an NH system by coupling a two-dimensional semiconductor with Rashba spin-orbit coupling (SOC) to a ferromagnet lead and show the emergence of highly tunable EPs along rings in momentum space. Interestingly, these exceptional degeneracies are the endpoints of lines formed by the eigenvalue coalescence at finite real energy, resembling the bulk Fermi arcs commonly defined at zero real energy. We then show that an in-plane Zeeman field provides a way to control these exceptional degeneracies although higher values of non-Hermiticity are required in contrast to the zero Zeeman field regime. Furthermore, we find that the spin projections also coalescence at the exceptional degeneracies and can acquire larger values than in the Hermitian regime. Finally, we demonstrate that the exceptional degeneracies induce large spectral weights, which can be used as a signature for their detection. Our results thus reveal the potential of systems with Rashba SOC for realizing NH bulk phenomena.
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Affiliation(s)
- Jorge Cayao
- Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
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9
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Wang C, Liu C, Shi ZY. Complex Contact Interaction for Systems with Short-Range Two-Body Losses. PHYSICAL REVIEW LETTERS 2022; 129:203401. [PMID: 36462004 DOI: 10.1103/physrevlett.129.203401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Revised: 04/26/2022] [Accepted: 10/10/2022] [Indexed: 06/17/2023]
Abstract
The concept of contact interaction is fundamental in various areas of physics. It simplifies physical models by replacing the detailed short-range interaction with a zero-range contact potential that reproduces the same low-energy scattering parameter, i.e., the s-wave scattering length. In this Letter, we generalize this concept to open quantum systems with short-range two-body losses. We show that the short-range two-body losses can be effectively described by a complex scattering length. However, in contrast to closed systems, the dynamics of an open quantum system is governed by the Lindblad master equation the includes a non-Hermitian Hamiltonian as well as an extra recycling term. We thus develop proper methods to regularize both terms in the master equation in the contact (zero-range) limit. We then apply our regularized complex contact interaction to study the dynamic problem of a weakly interacting and dissipating Bose-Einstein condensate. It is found that the physics is greatly enriched because the scattering length is continued from the real axis to the complex plane. For example, we show that a strong dissipation may prevent an attractive Bose-Einstein condensate from collapsing. We further calculate the particle decay in this system to the order of (density)^{3/2} which resembles the celebrated Lee-Huang-Yang correction to the ground state energy of interacting Bose gases [Lee and Yang, Phys. Rev. 105, 1119 (1957)PHRVAO0031-899X10.1103/PhysRev.105.1119; Lee, Huang, and Yang, Phys. Rev. 106, 1135 (1957)PHRVAO0031-899X10.1103/PhysRev.106.1135]. Possible methods for tuning the complex scattering length in cold atomic gas experiments are also discussed.
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Affiliation(s)
- Ce Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Chang Liu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhe-Yu Shi
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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10
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Lu M, Zhang XX, Franz M. Magnetic Suppression of Non-Hermitian Skin Effects. PHYSICAL REVIEW LETTERS 2021; 127:256402. [PMID: 35029425 DOI: 10.1103/physrevlett.127.256402] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 10/27/2021] [Indexed: 06/14/2023]
Abstract
Skin effect, where macroscopically many bulk states are aggregated toward the system boundary, is one of the most important and distinguishing phenomena in non-Hermitian quantum systems. We discuss a new aspect of this effect whereby, despite its topological origin, applying a magnetic field can largely suppress it. Skin states are pushed back into the bulk, and the skin topological area, which we define, is sharply reduced. As seen from exact solutions of representative models, this is fundamentally rooted in the fact that the applied magnetic field restores the validity of the low-energy description that is rendered inapplicable in the presence of non-Bloch skin states. We further study this phenomenon using rational gauge fluxes, which reveals a unique irrelevance of the generalized Brillouin zone in the standard non-Bloch band theory of non-Hermitian systems.
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Affiliation(s)
- Ming Lu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Xiao-Xiao Zhang
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Marcel Franz
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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Guo YB, Yu YC, Huang RZ, Yang LP, Chi RZ, Liao HJ, Xiang T. Entanglement entropy of non-Hermitian free fermions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:475502. [PMID: 34438384 DOI: 10.1088/1361-648x/ac216e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 08/26/2021] [Indexed: 06/13/2023]
Abstract
We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. For any one-dimensional one-band system, we prove that each Fermi point of the system contributes exactly 1/2 to the coefficientcof the logarithmic correction. Moreover, this relation betweencand Fermi point is verified for more general one-dimensional and two-dimensional cases by numerical calculations and finite-size scaling analysis. In addition, we also study the single-particle and density-density correlation functions.
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Affiliation(s)
- Yi-Bin Guo
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yi-Cong Yu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, IAPMST, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
| | - Rui-Zhen Huang
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Li-Ping Yang
- Department of Physics, Chongqing University, Chongqing 401331, People's Republic of China
| | - Run-Ze Chi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Hai-Jun Liao
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, People's Republic of China
| | - Tao Xiang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People's Republic of China
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12
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Bao XX, Guo GF, Tan L. Exploration of the topological properties in a non-Hermitian long-range system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:465403. [PMID: 34425563 DOI: 10.1088/1361-648x/ac2040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 08/23/2021] [Indexed: 06/13/2023]
Abstract
The asymmetrical long-range hopping amplitudes have a rich influence on the topological properties. Here, a non-Hermitian model including the long-range hopping amplitudes is constructed to explore those properties. It can be found that an extra topological invariantW= 2 emerges as a consequence of the long-range hopping amplitudes. Furthermore, we find that the phaseW= 2 can be directly characterized by the generalized Brillouin zone (GBZ) itself through the concept of the argument principle. Meanwhile, a gapless phase dubbed as topological semimetal phase can be induced by the asymmetrical long-range hopping. Moreover, the physical origin of the topological semimetal phase can be explained by the solutions of eigen-equation. It is also shown that the skin modes exist as long as the GBZ and the Brillouin zone differ from each other. These interesting phases may be realized in an electrical-circuit simulator.
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Affiliation(s)
- Xi-Xi Bao
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
| | - Gang-Feng Guo
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
| | - Lei Tan
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
- Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, People's Republic of China
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13
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Yamamoto K, Nakagawa M, Tsuji N, Ueda M, Kawakami N. Collective Excitations and Nonequilibrium Phase Transition in Dissipative Fermionic Superfluids. PHYSICAL REVIEW LETTERS 2021; 127:055301. [PMID: 34397242 DOI: 10.1103/physrevlett.127.055301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 06/17/2021] [Indexed: 06/13/2023]
Abstract
We predict a new mechanism to induce collective excitations and a nonequilibrium phase transition of fermionic superfluids via a sudden switch on of two-body loss, for which we extend the BCS theory to fully incorporate a change in particle number. We find that a sudden switch on of dissipation induces an amplitude oscillation of the superfluid order parameter accompanied by a chirped phase rotation as a consequence of particle loss. We demonstrate that when dissipation is introduced to one of the two superfluids coupled via a Josephson junction, it gives rise to a nonequilibrium dynamical phase transition characterized by the vanishing dc Josephson current. The dissipation-induced collective modes and nonequilibrium phase transition can be realized with ultracold fermionic atoms subject to inelastic collisions.
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Affiliation(s)
- Kazuki Yamamoto
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Naoto Tsuji
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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14
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Liu YG, Xu L, Li Z. Quantum phase transition in a non-Hermitian XYspin chain with global complex transverse field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:295401. [PMID: 33984851 DOI: 10.1088/1361-648x/ac00dd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 05/13/2021] [Indexed: 06/12/2023]
Abstract
In this work, we investigate the quantum phase transition in a non-HermitianXYspin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditionalXYmodel. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.
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Affiliation(s)
- Yu-Guo Liu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Lu Xu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Zhi Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, People's Republic of China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, People's Republic of China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, People's Republic of China
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15
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Nakagawa M, Kawakami N, Ueda M. Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model. PHYSICAL REVIEW LETTERS 2021; 126:110404. [PMID: 33798340 DOI: 10.1103/physrevlett.126.110404] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
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Affiliation(s)
- Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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16
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Matsumoto N, Kawabata K, Ashida Y, Furukawa S, Ueda M. Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2020; 125:260601. [PMID: 33449745 DOI: 10.1103/physrevlett.125.260601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Accepted: 11/17/2020] [Indexed: 06/12/2023]
Abstract
Contrary to the conventional wisdom in Hermitian systems, a continuous quantum phase transition between gapped phases is shown to occur without closing the energy gap Δ in non-Hermitian quantum many-body systems. Here, the relevant length scale ξ≃v_{LR}/Δ diverges because of the breakdown of the Lieb-Robinson bound on the velocity (i.e., unboundedness of v_{LR}) rather than vanishing of the energy gap Δ. The susceptibility to a change in the system parameter exhibits a singularity due to nonorthogonality of eigenstates. As an illustrative example, we present an exactly solvable model by generalizing Kitaev's toric-code model to a non-Hermitian regime.
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Affiliation(s)
- Norifumi Matsumoto
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kohei Kawabata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Yuto Ashida
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Shunsuke Furukawa
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
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17
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He M, Lv C, Lin HQ, Zhou Q. Universal relations for ultracold reactive molecules. SCIENCE ADVANCES 2020; 6:6/51/eabd4699. [PMID: 33355137 DOI: 10.1126/sciadv.abd4699] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.
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Affiliation(s)
- Mingyuan He
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
- Shenzhen JL Computational Science and Applied Research Institute, Shenzhen 518109, China
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Chenwei Lv
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
| | - Hai-Qing Lin
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA.
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
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18
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Yi Y, Yang Z. Non-Hermitian Skin Modes Induced by On-Site Dissipations and Chiral Tunneling Effect. PHYSICAL REVIEW LETTERS 2020; 125:186802. [PMID: 33196238 DOI: 10.1103/physrevlett.125.186802] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2020] [Accepted: 09/21/2020] [Indexed: 06/11/2023]
Abstract
In this Letter, we study the conditions under which on-site dissipations can induce non-Hermitian skin modes in non-Hermitian systems. When the original Hermitian Hamiltonian has spinless time-reversal symmetry, it is impossible to have skin modes; on the other hand, if the Hermitian Hamiltonian has spinful time-reversal symmetry, skin modes can be induced by on-site dissipations under certain circumstances. As a concrete example, we employ the Rice-Mele model to illustrate our results. Furthermore, we predict that the skin modes can be detected by the chiral tunneling effect; that is, the tunneling favors the direction where the skin modes are localized. Our Letter reveals a no-go theorem for the emergence of skin modes and paves the way for searching for quantum systems with skin modes and studying their novel physical responses.
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Affiliation(s)
- Yifei Yi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhesen Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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19
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Li L, Lee CH, Gong J. Topological Switch for Non-Hermitian Skin Effect in Cold-Atom Systems with Loss. PHYSICAL REVIEW LETTERS 2020; 124:250402. [PMID: 32639752 DOI: 10.1103/physrevlett.124.250402] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
We propose a realistic cold-atom quantum setting where topological localization induces nonreciprocal pumping. This is an intriguing non-Hermitian phenomenon that illustrates how topology, when assisted with atom loss, can act as a "switch" for the non-Hermitian skin effect (NHSE), rather than as a passive property that is modified by the NHSE. In particular, we present a lattice-shaking scenario to realize a two-dimensional cold-atom platform, where nonreciprocity is switched on only in the presence of both atom loss and topological localization due to time-reversal symmetry breaking. The resultant nonreciprocal pumping is manifested by asymmetric dynamical evolution, detectable by atomic populations along the system edges. Our setup may trigger possible applications in nonreciprocal atomtronics, where loss and topological mechanisms conspire to control atomic transport. Its quantum nature will also facilitate future studies on the interplay between non-Hermiticity and many-body physics.
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Affiliation(s)
- Linhu Li
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
| | - Ching Hua Lee
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore
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20
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Michishita Y, Peters R. Equivalence of Effective Non-Hermitian Hamiltonians in the Context of Open Quantum Systems and Strongly Correlated Electron Systems. PHYSICAL REVIEW LETTERS 2020; 124:196401. [PMID: 32469551 DOI: 10.1103/physrevlett.124.196401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Accepted: 04/20/2020] [Indexed: 06/11/2023]
Abstract
Recently, it has become clear that non-Hermitian phenomena can be observed not only in open quantum systems experiencing gain and loss but also in equilibrium single-particle properties of strongly correlated systems. However, the circumstances and requirements for the emergence of non-Hermitian phenomena in each field are entirely different. While the implementation of postselection is a significant obstacle to observe the dynamics governed by a non-Hermitian Hamiltonian in open quantum systems, it is unnecessary in strongly correlated systems. Until now, a relation between both descriptions of non-Hermitian phenomena has not been revealed. In this Letter, we close this gap and demonstrate that the non-Hermitian Hamiltonians emerging in both fields are identical, and we clarify the conditions for the emergence of a non-Hermitian Hamiltonian in strongly correlated materials. Using this knowledge, we propose a method to analyze non-Hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly correlated systems.
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Affiliation(s)
| | - Robert Peters
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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21
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Okuma N, Kawabata K, Shiozaki K, Sato M. Topological Origin of Non-Hermitian Skin Effects. PHYSICAL REVIEW LETTERS 2020; 124:086801. [PMID: 32167324 DOI: 10.1103/physrevlett.124.086801] [Citation(s) in RCA: 152] [Impact Index Per Article: 38.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/29/2020] [Indexed: 05/05/2023]
Abstract
A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects-symmetry-protected skin effects. In particular, we discover the Z_{2} skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.
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Affiliation(s)
- Nobuyuki Okuma
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Kohei Kawabata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ken Shiozaki
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masatoshi Sato
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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22
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Song F, Yao S, Wang Z. Non-Hermitian Topological Invariants in Real Space. PHYSICAL REVIEW LETTERS 2019; 123:246801. [PMID: 31922829 DOI: 10.1103/physrevlett.123.246801] [Citation(s) in RCA: 54] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2019] [Revised: 09/28/2019] [Indexed: 06/10/2023]
Abstract
The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topological invariants. In this Letter, we introduce a construction of non-Hermitian topological invariants based directly on real-space wave functions, which provides a general and straightforward approach for determining non-Hermitian topology. As an illustration, we apply this formulation to several representative models of non-Hermitian systems, efficiently obtaining their topological invariants in the presence of non-Hermitian skin effect. Our formulation also provides a dual picture of the non-Bloch band theory based on the generalized Brillouin zone, offering a unique perspective of bulk-boundary correspondence.
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Affiliation(s)
- Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Shunyu Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Stanford Institute for Theoretical Physics, Stanford University, Stanford California 94305, USA
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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23
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Yoshida T, Kudo K, Hatsugai Y. Non-Hermitian fractional quantum Hall states. Sci Rep 2019; 9:16895. [PMID: 31729412 PMCID: PMC6858315 DOI: 10.1038/s41598-019-53253-8] [Citation(s) in RCA: 59] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Accepted: 10/24/2019] [Indexed: 12/04/2022] Open
Abstract
We demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.
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Affiliation(s)
- Tsuneya Yoshida
- Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan.
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan.
| | - Koji Kudo
- Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan
| | - Yasuhiro Hatsugai
- Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan
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24
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Lee JY, Ahn J, Zhou H, Vishwanath A. Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics. PHYSICAL REVIEW LETTERS 2019; 123:206404. [PMID: 31809078 DOI: 10.1103/physrevlett.123.206404] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Indexed: 06/10/2023]
Abstract
The hallmark of symmetry-protected topological phases is the existence of anomalous boundary states, which can only be realized with the corresponding bulk system. In this work, we show that for every Hermitian anomalous boundary mode of the ten Altland-Zirnbauer classes, a non-Hermitian counterpart can be constructed, whose long-time dynamics provides a realization of the anomalous boundary state. We prove that the non-Hermitian counterpart is characterized by a point-gap topological invariant, and furthermore, that the invariant exactly matches that of the corresponding Hermitian anomalous boundary mode. We thus establish a correspondence between the topological classifications of (d+1)-dimensional gapped Hermitian systems and d-dimensional point-gapped non-Hermitian systems. We illustrate this general result with a number of examples in different dimensions. This work provides a new perspective on point-gap topological invariants in non-Hermitian systems.
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Affiliation(s)
- Jong Yeon Lee
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Junyeong Ahn
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
- Center for Theoretical Physics (CTP), Seoul National University, Seoul 08826, Korea
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ashvin Vishwanath
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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