Signatures of Nonergodicity in Sparse Random Matrices
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918401831600128 |
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| author | Seth, Sagnik Das, Adway Kumar Ghosh, Anandamohan |
| author_facet | Seth, Sagnik Das, Adway Kumar Ghosh, Anandamohan |
| contents | The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified through the statistical properties of the ground state. By analytically deriving the energy moments and calculating the shifted kurtosis, we estimate the critical sparsity threshold for this localization-delocalization transition. The short-range energy correlation in the bulk indicates that the Anderson transition at infinite temperature coincides with the quantum phase transition. Furthermore, long-range energy correlations in the bulk spectrum reveal a Thouless energy scale, suggesting a broad nonergodic regime within the delocalized phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signatures of Nonergodicity in Sparse Random Matrices Seth, Sagnik Das, Adway Kumar Ghosh, Anandamohan Disordered Systems and Neural Networks Statistical Mechanics The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified through the statistical properties of the ground state. By analytically deriving the energy moments and calculating the shifted kurtosis, we estimate the critical sparsity threshold for this localization-delocalization transition. The short-range energy correlation in the bulk indicates that the Anderson transition at infinite temperature coincides with the quantum phase transition. Furthermore, long-range energy correlations in the bulk spectrum reveal a Thouless energy scale, suggesting a broad nonergodic regime within the delocalized phase. |
| title | Signatures of Nonergodicity in Sparse Random Matrices |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2603.21369 |