Universal hard-edge statistics of non-Hermitian random matrices
arXiv:2401.05044 · doi:10.1103/PhysRevResearch.6.023303
Abstract
Random matrix theory is a powerful tool for understanding spectral correlations inherent in quantum chaotic systems. Despite diverse applications of non-Hermitian random matrix theory, the role of symmetry remains to be fully established. Here, we comprehensively investigate the impact of symmetry on the level statistics around the spectral origin -- hard-edge statistics -- and expand the classification of spectral statistics to encompass all the 38 symmetry classes of non-Hermitian random matrices. Within this classification, we discern 28 symmetry classes characterized by distinct hard-edge statistics from the level statistics in the bulk of spectra, which are further categorized into two groups, namely the Altland-Zirnbauer classification and beyond. We introduce and elucidate quantitative measures capturing the universal hard-edge statistics for all the symmetry classes. Furthermore, through extensive numerical calculations, we study various open quantum systems in different symmetry classes, including quadratic and many-body Lindbladians, as well as non-Hermitian Hamiltonians. We show that these systems manifest the same hard-edge statistics as random matrices and that their ensemble-average spectral distributions around the origin exhibit emergent symmetry conforming to the random-matrix behavior. Our results establish a comprehensive understanding of non-Hermitian random matrix theory and are useful in detecting quantum chaos or its absence in open quantum systems.
References in corpus (29)
- Classification of topological insulators and superconductors in three spatial dimensions
- Making Sense of Non-Hermitian Hamiltonians
- Many body localization and thermalization in quantum statistical mechanics
- Anderson Transitions
- Localization of interacting fermions at high temperature
- Topological Origin of Non-Hermitian Skin Effects
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Quantum trajectories and open many-body quantum systems
- Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
- Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Topological phase transition in non-Hermitian quasicrystals
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Topological quantum matter in synthetic dimensions
- Photonic Topological Anderson Insulators
- Synthetic dimensions and spin-orbit coupling with an optical clock transition
- Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
- Anderson transition in three-dimensional systems with non-Hermitian disorder
- Many-body localization in a non-Hermitian quasi-periodic system
- Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
- PT-symmetric quantum Liouvillian dynamics
- Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
- Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
- Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
- Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
- Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
- Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
- Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
- Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes