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Article Dans Une Revue SciPost Physics Année : 2023

Replica approach to the generalized Rosenzweig-Porter model

Résumé

The generalized Rosenzweig-Porter model arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first derive analytical expressions for the average spectral density in the limit in which the size $N$ of the matrix is large but finite. We then focus on the number of eigenvalues in a finite interval and compute its cumulant generating function as well as the level compressibility, i.e., the ratio of the first two cumulants: these are useful tools to describe the local level statistics. In particular, the level compressibility is shown to be described by a universal scaling function, which we compute explicitly, when the system is probed over scales of the order of the Thouless energy. We confirm our results with numerical tests.
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hal-03814029 , version 1 (16-12-2023)

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Davide Venturelli, Leticia F. Cugliandolo, Grégory Schehr, Marco Tarzia. Replica approach to the generalized Rosenzweig-Porter model. SciPost Physics, 2023, 14 (5), pp.110. ⟨10.21468/SciPostPhys.14.5.110⟩. ⟨hal-03814029⟩
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