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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.04665 |
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| _version_ | 1866914668611633152 |
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| author | Xue, Qiaomu Rao, Wenjia |
| author_facet | Xue, Qiaomu Rao, Wenjia |
| contents | Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms such as singular-value-decomposition has proven its advantage in studying subtle physical quantities like Thouless energy and non-ergodic extended regime. On the other hand, algorithms from complex networks have long been known as a powerful tool to study highly nonlinear time-series. In this work, we combine these two ideas together. Using the particular algorithm called visibility graph (VG) that transforms the eigenvalue spectra of a random spin system into complex networks, it's shown the degree distribution of the resulting network is capable of signaturing the eigenvalue evolution during the thermal to many-body localization transition, and the networks in the thermal phase have a small-world structure. We further show these results are robust even when the eigenvalues are incomplete with missing levels, which reveals the advantage of the VG algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04665 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems Xue, Qiaomu Rao, Wenjia Disordered Systems and Neural Networks Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms such as singular-value-decomposition has proven its advantage in studying subtle physical quantities like Thouless energy and non-ergodic extended regime. On the other hand, algorithms from complex networks have long been known as a powerful tool to study highly nonlinear time-series. In this work, we combine these two ideas together. Using the particular algorithm called visibility graph (VG) that transforms the eigenvalue spectra of a random spin system into complex networks, it's shown the degree distribution of the resulting network is capable of signaturing the eigenvalue evolution during the thermal to many-body localization transition, and the networks in the thermal phase have a small-world structure. We further show these results are robust even when the eigenvalues are incomplete with missing levels, which reveals the advantage of the VG algorithm. |
| title | A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2311.04665 |