Perturbation Theory for the Rosenzweig-Porter Matrix Model

TL;DR

This paper applies diagrammatic perturbation theory to analyze the level correlations of the non-invariant Rosenzweig-Porter random matrix model, providing a physical interpretation of its spectral structure.

Contribution

It introduces a perturbative approach to understand the spectral correlations of the Rosenzweig-Porter model, which lacks basis invariance.

Findings

Complete understanding of level correlations achieved

Perturbation expansion offers physical insights

Analysis extends beyond invariant ensembles

Abstract

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can be obtained within the standard framework of diagrammatic perturbation theory. The structure of the perturbation expansion allows for an interpretation of the level structure on simple physical grounds, an aspect that is missing in the exact analysis (T. Guhr, Phys. Rev. Lett. 76, 2258 (1996), T. Guhr and A. M\"uller-Groeling, cond-mat/9702113).