Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Lunkin, A. V. Tikhonov, K. S. |
| author_facet | Lunkin, A. V. Tikhonov, K. S. |
| contents | We present an analytical calculation of the local density of states correlation function $ β(ω) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $Γ_0$. We show that $β(ω\ll Γ_0) \sim W/Γ_0$ (here $W$ is width of the band) whereas $β(ω\gg Γ_0) \sim (W/Γ_0) (ω/Γ_0)^{-μ} $ where $μ$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\ggΓ_0^{-1})] \sim -(Γ_0 t)^{μ/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble Lunkin, A. V. Tikhonov, K. S. Disordered Systems and Neural Networks We present an analytical calculation of the local density of states correlation function $ β(ω) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $Γ_0$. We show that $β(ω\ll Γ_0) \sim W/Γ_0$ (here $W$ is width of the band) whereas $β(ω\gg Γ_0) \sim (W/Γ_0) (ω/Γ_0)^{-μ} $ where $μ$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\ggΓ_0^{-1})] \sim -(Γ_0 t)^{μ/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory. |
| title | Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2410.14437 |