Disorder in Gauge/Gravity Duality, Pole Spectrum Statistics and Random Matrix Theory

TL;DR

This paper investigates phase transitions in disordered large-N gauge theories with gravity duals, revealing phases with Poisson-distributed pole spectra akin to localized states in condensed matter systems.

Contribution

It provides evidence for distinct spectral phases in a gauge/gravity duality model, connecting disorder, spectral statistics, and phase characterization.

Findings

Existence of phases with Poisson spectral statistics

Spectral rigidity and chi-squared tests support phase distinction

Pole spectra can be regular or uncorrelated depending on disorder

Abstract

In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of Random Matrix Theory, the so-called $\bar{\Delta_3}$, or spectral rigidity, proposed by Dyson and Mehta. The second is a $\chi$-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.