Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912673071890432 |
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| author | Kulkarni, Anish Kawabata, Kohei Ryu, Shinsei |
| author_facet | Kulkarni, Anish Kawabata, Kohei Ryu, Shinsei |
| contents | Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS$^{\dagger}$ with signs $+1$ and $-1$, corresponding to symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$, respectively. Using the fermionic replica non-linear sigma model approach, we derive $n$-fold integral expressions for the $n$th moment of the one-point and two-point characteristic polynomials. Performing the replica limit $n\to 0$, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS$^{\dagger}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$ Kulkarni, Anish Kawabata, Kohei Ryu, Shinsei Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Chaotic Dynamics Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS$^{\dagger}$ with signs $+1$ and $-1$, corresponding to symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$, respectively. Using the fermionic replica non-linear sigma model approach, we derive $n$-fold integral expressions for the $n$th moment of the one-point and two-point characteristic polynomials. Performing the replica limit $n\to 0$, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS$^{\dagger}$. |
| title | Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$ |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2410.24043 |