Random Matrices with Correlated Elements: A Model for Disorder with Interactions

TL;DR

This paper models disordered interacting systems using correlated random matrices and demonstrates that their eigenvalue correlations can be described by Brownian ensembles, revealing unique spectral features and phase behaviors.

Contribution

It introduces a correlated random matrix model for disordered interacting systems and links their eigenvalue statistics to Brownian ensembles, highlighting new spectral phenomena.

Findings

Eigenvalue correlations follow single parametric Brownian ensemble behavior.

Identification of a critical point behavior distinct from non-interacting systems.

Potential for extended states in one-dimensional disordered interacting systems.

Abstract

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations of these matrices can be described by the single parametric Brownian ensembles. The analogy helps us to reveal many important features of the level-statistics in interacting systems e.g. a critical point behavior different from that of non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level correlations.