Universal hard-edge statistics of non-Hermitian random matrices

• URL: http://arxiv.org/abs/2401.05044v2
• Date: Sat, 1 Jun 2024 05:44:26 GMT
• Title: Universal hard-edge statistics of non-Hermitian random matrices
• Authors: Zhenyu Xiao, Ryuichi Shindou, Kohei Kawabata,
• Abstract summary: We investigate the impact of symmetry on the level statistics around the spectral origin. Within this classification, we discern 28 symmetry classes characterized by distinct hard-edge statistics. We study various open quantum systems in different symmetry classes, including quadratic and many-body Lindbladians.
• Score: 4.794899293121226
• License: http://creativecommons.org/licenses/by/4.0/
• 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$_0$ 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.

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