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Review
Physics, Condensed Matter
Matthew P. A. Fisher et al.
Summary: Quantum circuits, constructed from local unitary gates and local measurements, have become a useful tool in studying universal collective phenomena in non-equilibrium conditions. These models have provided insights into long-standing questions regarding thermalization, chaos, and the dynamics of quantum information and entanglement. Additionally, they have led to the discovery of new phenomena, such as dynamical phase transitions, that do not have traditional analogues. The randomness of the circuit elements allows for increased theoretical control and the mapping of real-time quantum dynamics to classical lattice models or dynamical processes.
ANNUAL REVIEW OF CONDENSED MATTER PHYSICS
(2023)
Article
Physics, Particles & Fields
Apollonas S. Matsoukas-Roubeas et al.
Summary: This research considers a broad class of non-Hermitian Hamiltonian deformations in a nonrelativistic setting, which can describe a large class of open quantum systems, including arbitrary Markovian evolutions conditioned to the absence of quantum jumps. The time evolution operator and time-evolving density matrix in the undeformed and deformed theories are related through integral transforms with a specific kernel. Non-Hermitian Hamiltonian deformations naturally arise in the description of energy diffusion due to time-keeping errors in a real clock used for time evolution tracking. The spectral properties of the dynamical generators associated with the deformed theories are also studied.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Review
Physics, Condensed Matter
Nobuyuki Okuma et al.
Summary: The past decades have witnessed a strong interest in topological materials and the introduction of mathematical concepts in condensed matter physics. The bulk-boundary correspondence is a central topic in topological physics, inspiring researchers to focus on boundary physics. Recently, the concept of topological phases has been extended to non-Hermitian Hamiltonians, where eigenvalues can be complex. In addition to the topology, non-Hermiticity also causes the non-Hermitian skin effect, an extreme sensitivity of the spectrum to the boundary condition. In this article, we review the developments in non-Hermitian topological physics, with a focus on the boundary problem and the interplay between non-Hermitian and topological boundary phenomena.
ANNUAL REVIEW OF CONDENSED MATTER PHYSICS
(2023)
Article
Physics, Multidisciplinary
Saumya Shivam et al.
Summary: We demonstrate that non-Hermitian Ginibre random matrix behaviors can be observed in spatially extended many-body quantum chaotic systems. This is similar to the emergence of Hermitian random matrix behaviors in chaotic systems. By studying translational invariant models, we show that the dual spectra have nontrivial correlations, falling into the universality class of the Ginibre ensemble. This connection allows us to use the exact spectral form factor for the Ginibre ensemble to describe the spectral form factor for translational invariant many-body quantum chaotic systems.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Lucas Sa et al.
Summary: In this study, we systematically classify many-body Lindblad superoperators describing open quantum systems based on their behavior under antiunitary symmetries and unitary involutions. We find that the preservation of certain properties reduces the number of symmetry classes, and the presence of additional symmetries can lead to different sets of classes. The classification is applicable to both Markovian and non-Markovian dynamics.
Article
Quantum Science & Technology
Kohei Kawabata et al.
Summary: This article develops a theory of symmetry in open quantum systems and investigates the symmetry classification of different types of open quantum systems. The results indicate that symmetry plays a crucial role in open quantum systems and enriches the dynamics of the systems.
Article
Physics, Multidisciplinary
Antonio M. Garcia-Garcia et al.
Summary: We demonstrate that the low temperature phase of uncoupled, quantum chaotic, non-Hermitian systems such as the SYK model or the Ginibre ensemble of random matrices is governed by saddle points that couple replicas and conjugate replicas after ensemble averaging. This leads to an almost flat free energy that terminates in a first-order phase transition. In the case of the SYK model, we explicitly show that the spectrum of the effective replica theory has a gap. These features resemble those induced by wormholes in the gravity path integral, suggesting a strong connection between these configurations. For a nonchaotic SYK model, the results differ qualitatively with a gapless spectrum in the low temperature phase and an infinite number of second order phase transitions unrelated to replica symmetry restoration.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Julien Cornelius et al.
Summary: The study finds that balanced gain and loss in non-Hermitian evolution can enhance the manifestation of quantum chaos and provide a feasible experimental mechanism for spectral filtering.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Antonio M. Garcia-Garcia et al.
Summary: Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. This study shows that local level statistics of a non-Hermitian q-body Sachdev-Ye-Kitev (nHSYK) model can be well described by random matrix theory, providing evidence of universal features in nonunitary many-body quantum chaos. The study also identifies 19 out of the 38 non-Hermitian universality classes in the nHSYK model.
Article
Physics, Multidisciplinary
Zhenyu Xiao et al.
Summary: In this study, the authors investigate the universal level statistics of non-Hermitian random matrices and analyze the spacings of real eigenvalues in physical models. The results provide effective tools for detecting quantum chaos, many-body localization, and real-complex transitions in non-Hermitian systems with symmetries.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Materials Science, Multidisciplinary
Anish Kulkarni et al.
Summary: In this study, the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model coupled to Markovian reservoirs with different types of jump operators was investigated. Analytical results for the stationary Green's functions and decay rates of the SYK Lindbladians were obtained in the large N and large N/M limits. The distribution of eigenvalues of SYK Lindbladians for finite N was also analyzed.
Article
Materials Science, Multidisciplinary
Soumi Ghosh et al.
Summary: This study analyzes the chaotic behavior of non-Hermitian interacting disordered Hamiltonians through the non-Hermitian analog of the spectral form factor and the complex spacing ratio. The findings are expected to play a crucial role in understanding disordered open quantum systems in general.
Article
Astronomy & Astrophysics
Antonio M. Garcia-Garcia et al.
Summary: Recent studies have found intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. By investigating a PT-symmetric system composed of two random non-Hermitian Hamiltonians, we have identified a robust first-order phase transition in the free energy and obtained analytical expressions for the critical temperature. The mechanism behind the transition is controlled by replica symmetry breaking configurations.
Article
Physics, Multidisciplinary
Lucas Sa et al.
Summary: In this letter, the authors propose the Sachdev-Ye-Kitaev Lindbladian as a solvable model to study dissipative many-body quantum chaos. They develop a mean-field theory and derive the effective action for collective fields, which are determined by solving the saddle-point equations. The results provide insights into the relaxation dynamics of the system.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Physics, Multidisciplinary
Xunlong Luo et al.
Summary: This study proposes a correspondence between the universality classes of the Anderson transitions in Hermitian and non-Hermitian systems, showcasing the superuniversality phenomenon.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Physics, Multidisciplinary
Jiachen Li et al.
Summary: The DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between complex eigenvalues; for dissipative quantum chaotic systems, the DSFF exhibits exact rotational symmetry and unique evolution features; for dissipative quantum integrable systems, the DSFF takes a constant value except for specific behaviors in certain regions of complex time.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Xunlong Luo et al.
Summary: The study explores the influence of non-Hermiticity and disorder on Anderson transitions in three-dimensional systems, finding distinct critical behaviors and key exponents under different classifications of non-Hermitian systems, demonstrating that non-Hermiticity changes the universality classes of Anderson transitions.
PHYSICAL REVIEW LETTERS
(2021)
Review
Physics, Multidisciplinary
Emil J. Bergholtz et al.
Summary: This review discusses the current understanding of the role of topology in non-Hermitian systems and its physical consequences in dissipative settings, focusing on the concept of exceptional degeneracies and its distinct phenomena, as well as the new notions of gapped phases in single-band systems. The unique sensitivity of non-Hermitian matrices to boundary conditions is highlighted, leading to anomalous relationships between bulk and boundary physics. Additionally, applications of non-Hermitian topology in classical and quantum systems are reviewed, showing its relevance beyond the field of topological phases.
REVIEWS OF MODERN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Kohei Kawabata et al.
Summary: The authors developed a scaling theory of localization in non-Hermitian systems, revealing that non-Hermiticity introduces a new scale and breaks down the conventional one-parameter scaling theory of localization. The unconventional non-Hermitian delocalization is identified as originating from the two-parameter scaling. Furthermore, based on reciprocity, the authors established the threefold universality of non-Hermitian localization, where reciprocity prohibits delocalization without internal degrees of freedom, and symplectic reciprocity results in a new type of symmetry-protected delocalization.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Heinrich-Gregor Zirnstein et al.
Summary: This study investigates the realization of genuinely non-Hermitian topological phases in open systems with strong gain and loss, and reveals that the non-Hermitian winding number in one dimension indicates a topological phase transition in the bulk, implying spatial growth of the bulk Green function.
PHYSICAL REVIEW LETTERS
(2021)
Article
Materials Science, Multidisciplinary
Hui Liu et al.
Summary: We studied a non-Hermitian and nonunitary version of the two-dimensional Chalker-Coddington network model with balanced gain and loss, and found a contact effect induced by the skin effect in the two-terminal transmission, as well as an insulator to supermetal transition.
Article
Materials Science, Multidisciplinary
Xunlong Luo et al.
Summary: The paper presents a detailed transfer matrix analysis of the Anderson transition driven by non-Hermitian disorder in three NH systems. It discusses the general validity of the transfer matrix analysis in NH systems and analyzes the symmetry properties of the Lyapunov exponents, scattering matrix, and two-terminal conductance in these NH models. The study shows violations of unitarity in the S matrix in NH systems and the symmetric nature of the S matrix, Lyapunov exponents, and conductance in certain NH models.
Article
Physics, Fluids & Plasmas
W. Tarnowski et al.
Summary: By studying ensembles of quantum and classical random generators of N-dimensional Markovian evolution, we demonstrate the relationship between the two types of generators through superdecoherence. Increasing the strength of superdecoherence gradually leads to a sharp quantum-to-classical transition. Additionally, microscopic correlation between neighboring eigenvalues and the presence of horseshoe distribution, emblematic of the Ginibre universality class, is observed in both types of random generators even under superdecoherence and supercoherification.
Article
Materials Science, Multidisciplinary
Heinrich-Gregor Zirnstein et al.
Summary: Analyzing the bulk Green function reveals that a nonzero non-Hermitian winding number leads to spatial growth in the system's bulk response, explaining the sensitivity of non-Hermitian systems to boundary conditions on longer timescales and the breakdown of bulk-boundary correspondence.
Article
Materials Science, Multidisciplinary
Zhenyu Xu et al.
Summary: Quantum chaos imposes universal spectral signatures on the thermofield dynamics of many-body systems in isolation. The interplay between quantum chaos and information loss is determined by the competition among characteristic times of decoherence, dip, and plateau. Energy dephasing gradually suppresses quantum noise fluctuations and delays the appearance of the dip associated with spectral correlations.
Article
Physics, Multidisciplinary
Lucas Sa et al.
Article
Physics, Multidisciplinary
Kevin Wang et al.
PHYSICAL REVIEW LETTERS
(2020)
Article
Physics, Multidisciplinary
Fadi Sun et al.
PHYSICAL REVIEW LETTERS
(2020)
Article
Physics, Multidisciplinary
Ryusuke Hamazaki et al.
PHYSICAL REVIEW RESEARCH
(2020)
Article
Materials Science, Multidisciplinary
A. F. Tzortzakakis et al.
Article
Materials Science, Multidisciplinary
Yi Huang et al.
Article
Physics, Multidisciplinary
S. Longhi
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Multidisciplinary
Ryusuke Hamazaki et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Multidisciplinary
Sergey Denisov et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Multidisciplinary
Tankut Can
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2019)
Article
Physics, Multidisciplinary
Kohei Kawabata et al.
Article
Physics, Multidisciplinary
Zhenyu Xu et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Multidisciplinary Sciences
Kohei Kawabata et al.
NATURE COMMUNICATIONS
(2019)
Article
Physics, Multidisciplinary
Tankut Can et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Multidisciplinary
Gernot Akemann et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Materials Science, Multidisciplinary
Hengyun Zhou et al.
Article
Optics
Loic Herviou et al.
Article
Physics, Fluids & Plasmas
Ryusuke Hamazaki et al.
Review
Physics, Multidisciplinary
Ramy El-Ganainy et al.
Article
Physics, Multidisciplinary
Zongping Gong et al.
Article
Physics, Condensed Matter
Luca D'Alessio et al.
ADVANCES IN PHYSICS
(2016)
Article
Physics, Multidisciplinary
Vladimir V. Konotop et al.
REVIEWS OF MODERN PHYSICS
(2016)
Article
Physics, Multidisciplinary
Ching-Kai Chiu et al.
REVIEWS OF MODERN PHYSICS
(2016)
Article
Physics, Multidisciplinary
C. W. J. Beenakker
REVIEWS OF MODERN PHYSICS
(2015)
Review
Physics, Condensed Matter
Rahul Nandkishore et al.
ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 6
(2015)
Review
Physics, Condensed Matter
Andrew J. Daley
ADVANCES IN PHYSICS
(2014)
Article
Physics, Multidisciplinary
Y. Y. Atas et al.
PHYSICAL REVIEW LETTERS
(2013)
Article
Physics, Multidisciplinary
Xiao-Liang Qi et al.
REVIEWS OF MODERN PHYSICS
(2011)
Article
Physics, Multidisciplinary
Shinsei Ryu et al.
NEW JOURNAL OF PHYSICS
(2010)
Article
Physics, Multidisciplinary
M. Z. Hasan et al.
REVIEWS OF MODERN PHYSICS
(2010)
Article
Materials Science, Multidisciplinary
Andreas P. Schnyder et al.
Review
Physics, Multidisciplinary
Ferdinand Evers et al.
REVIEWS OF MODERN PHYSICS
(2008)
Review
Physics, Multidisciplinary
Carl M. Bender
REPORTS ON PROGRESS IN PHYSICS
(2007)
Article
Materials Science, Multidisciplinary
Vadim Oganesyan et al.
Article
Physics, Mathematical
P Elbau et al.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2005)
Article
Physics, Mathematical
A Mostafazadeh
JOURNAL OF MATHEMATICAL PHYSICS
(2002)
Article
Physics, Mathematical
A Mostafazadeh
JOURNAL OF MATHEMATICAL PHYSICS
(2002)
Article
Astronomy & Astrophysics
PH Damgaard et al.