# Supersymmetric Virial Expansion for Time-Reversal Invariant Disordered Systems

## TL;DR

This paper introduces a supersymmetric virial expansion method for analyzing two-point correlation functions in orthogonal symmetry Gaussian random matrix ensembles, with applications to disordered systems near localization transitions.

## Contribution

It develops a novel supersymmetric virial expansion approach for ADRMTs and applies it to critical power-law banded ensembles, bridging analytical and numerical results.

## Key findings

- Derived a two-level correlation function contribution for ADRMT.
- Applied the method to critical power-law banded ensembles.
- Validated analytical results with numerical simulations.

## Abstract

We develop a supersymmetric virial expansion for two point correlation functions of almost diagonal Gaussian Random Matrix Ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple applications in physics and can be used to study universal properties of time-reversal invariant disordered systems which are either insulators or close to the Anderson localization transition. We derive a two-level contribution to the correlation functions of the generic ADRMT and apply these results to the critical (multifractal) power law banded ADRMT. Analytical results are compared with numerical ones.