Level statistics of real eigenvalues in non-Hermitian systems
Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have a great impact on the eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal symmetry and pseudo-Hermiticity lead to universal level st...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043196 |
| _version_ | 1827285333662760960 |
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| author | Zhenyu Xiao Kohei Kawabata Xunlong Luo Tomi Ohtsuki Ryuichi Shindou |
| author_facet | Zhenyu Xiao Kohei Kawabata Xunlong Luo Tomi Ohtsuki Ryuichi Shindou |
| author_sort | Zhenyu Xiao |
| collection | DOAJ |
| description | Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have a great impact on the eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal symmetry and pseudo-Hermiticity lead to universal level statistics of non-Hermitian random matrices on and around the real axis. From the extensive numerical calculations of large random matrices, we obtain the five universal level-spacing and level-spacing-ratio distributions of real eigenvalues, each of which is unique to the symmetry class. Furthermore, we analyze spacings of real eigenvalues in physical models, such as bosonic many-body systems and free fermionic systems with disorder and dissipation. We clarify that the level spacings in ergodic (metallic) phases are described by the universal distributions of non-Hermitian random matrices in the same symmetry classes, while the level spacings in many-body localized and Anderson localized phases show the Poisson statistics. We also find that the number of real eigenvalues shows distinct scalings in the ergodic and localized phases in these symmetry classes. These results serve as effective tools for detecting quantum chaos, many-body localization, and real-complex transitions in non-Hermitian systems with symmetries. |
| first_indexed | 2024-04-24T10:13:12Z |
| format | Article |
| id | doaj.art-b5df6d307e0f4276b36a101ae34dc5a6 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:12Z |
| publishDate | 2022-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-b5df6d307e0f4276b36a101ae34dc5a62024-04-12T17:27:06ZengAmerican Physical SocietyPhysical Review Research2643-15642022-12-014404319610.1103/PhysRevResearch.4.043196Level statistics of real eigenvalues in non-Hermitian systemsZhenyu XiaoKohei KawabataXunlong LuoTomi OhtsukiRyuichi ShindouSymmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have a great impact on the eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal symmetry and pseudo-Hermiticity lead to universal level statistics of non-Hermitian random matrices on and around the real axis. From the extensive numerical calculations of large random matrices, we obtain the five universal level-spacing and level-spacing-ratio distributions of real eigenvalues, each of which is unique to the symmetry class. Furthermore, we analyze spacings of real eigenvalues in physical models, such as bosonic many-body systems and free fermionic systems with disorder and dissipation. We clarify that the level spacings in ergodic (metallic) phases are described by the universal distributions of non-Hermitian random matrices in the same symmetry classes, while the level spacings in many-body localized and Anderson localized phases show the Poisson statistics. We also find that the number of real eigenvalues shows distinct scalings in the ergodic and localized phases in these symmetry classes. These results serve as effective tools for detecting quantum chaos, many-body localization, and real-complex transitions in non-Hermitian systems with symmetries.http://doi.org/10.1103/PhysRevResearch.4.043196 |
| spellingShingle | Zhenyu Xiao Kohei Kawabata Xunlong Luo Tomi Ohtsuki Ryuichi Shindou Level statistics of real eigenvalues in non-Hermitian systems Physical Review Research |
| title | Level statistics of real eigenvalues in non-Hermitian systems |
| title_full | Level statistics of real eigenvalues in non-Hermitian systems |
| title_fullStr | Level statistics of real eigenvalues in non-Hermitian systems |
| title_full_unstemmed | Level statistics of real eigenvalues in non-Hermitian systems |
| title_short | Level statistics of real eigenvalues in non-Hermitian systems |
| title_sort | level statistics of real eigenvalues in non hermitian systems |
| url | http://doi.org/10.1103/PhysRevResearch.4.043196 |
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