Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914252851249152 |
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| author | Safonova, Elizaveta Lunkin, Aleksey man, Mikhail Feigel' |
| author_facet | Safonova, Elizaveta Lunkin, Aleksey man, Mikhail Feigel' |
| contents | We studied global density-of-states correlation function $R(ω)$ for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(ω)$ exactly in all relevant ranges of $ω$. At relatively low $ω\leq Γ$\, (with $Γ\gg Δ$ being the effective miniband width) we found GUE-type oscillations with period of level spacing $Δ$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{ΔΓ/2π}$. At high energies $ω\gg E_{Th}$ our results coincide with those obtainen via cavity equation approach. Inverse of the effective miniband width, $1/Γ$, is shown to be given by the average of the local decay times over Lévy distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach Safonova, Elizaveta Lunkin, Aleksey man, Mikhail Feigel' Disordered Systems and Neural Networks Mathematical Physics We studied global density-of-states correlation function $R(ω)$ for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(ω)$ exactly in all relevant ranges of $ω$. At relatively low $ω\leq Γ$\, (with $Γ\gg Δ$ being the effective miniband width) we found GUE-type oscillations with period of level spacing $Δ$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{ΔΓ/2π}$. At high energies $ω\gg E_{Th}$ our results coincide with those obtainen via cavity equation approach. Inverse of the effective miniband width, $1/Γ$, is shown to be given by the average of the local decay times over Lévy distribution. |
| title | Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach |
| topic | Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2505.23903 |