Universal hard-edge statistics of non-Hermitian random matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910519235969024 |
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| author | Xiao, Zhenyu Shindou, Ryuichi Kawabata, Kohei |
| author_facet | Xiao, Zhenyu Shindou, Ryuichi Kawabata, Kohei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal hard-edge statistics of non-Hermitian random matrices Xiao, Zhenyu Shindou, Ryuichi Kawabata, Kohei Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics 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. |
| title | Universal hard-edge statistics of non-Hermitian random matrices |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2401.05044 |