Superbosonization formula and its application to random matrix theory

TL;DR

This paper introduces a new supermatrix field theory model derived from Gaussian random matrices, applicable across all correlation ranges, and demonstrates its utility by calculating the density of states for almost diagonal matrices.

Contribution

The paper develops a novel supermatrix model that extends beyond traditional sigma models, enabling analysis of correlated random matrices and providing a method to reduce to conventional models.

Findings

New supermatrix model applicable for any correlation range

Demonstrated calculation of density of states for almost diagonal matrices

Showed reduction method to conventional sigma models

Abstract

Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random matrices. We clarify the domain of integration for the supermatrices, and give a demonstration of how the model works by calculating the density of states for an ensemble of almost diagonal matrices. It is also shown how one can reduce the supermatrix model to the conventional sigma model.