Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition

Abstract

Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized (MBL) phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. Through the use of the singular value decomposition and the introduction of new diagnostic tools complementing the singular-value statistics, namely, the singular form factor, the inverse participation ratio, and entanglement entropy for singular vectors, we provide a positive answer. Our method is illustrated in an XXZ Hamiltonian with random local dissipation.

5+6 pages, 2+6 figures

References in corpus (15)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Integrals of motion in the Many-Body localized phase
• Ergodicity breaking in a model showing many-body localization
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Can we study the many-body localisation transition?
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Many-body localization in a non-Hermitian quasi-periodic system
• Many-body topology of non-Hermitian systems
• Quantum annealing: the fastest route to quantum computation?
• Topological input-output theory for directional amplification
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems

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• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models
• Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
• Expedited thermalization dynamics in incommensurate systems
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• Universal hard-edge statistics of non-Hermitian random matrices
• Higher-order gap ratios of singular values in open quantum systems
• Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
• Localization of Lindbladian Fermions
• Finite steady-state current defies non-Hermitian many-body localization
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Hard edge asymptotics of correlation functions between singular values and eigenvalues
• Correlation functions between singular values and eigenvalues
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry