Coherence effects in disordered geometries with a field-theory dual

TL;DR

This paper explores how disorder affects quantum correlations in a holographic model with a dual gravity description, revealing suppression effects and potential phase transitions due to disorder.

Contribution

It provides an analytical and numerical study of disorder effects on one- and two-point functions in a holographic setup, highlighting interference effects and phase transition indications.

Findings

Suppression of one-point function with oscillating sources and weak disorder

Disorder induces a power-law decay in two-point functions with variable exponents

Evidence of disorder-induced phase transition at large separations

Abstract

We investigate the holographic dual of a probe scalar in an asymptotically Anti-de-Sitter (AdS) disordered background which is an exact solution of Einstein's equations in three bulk dimensions. Unlike other approaches to model disorder in holography, we are able to explore quantum wave-like interference effects between an oscillating or random source and the geometry. In the weak-disorder limit, we compute analytically and numerically the one-point correlation function of the dual field theory for different choices of sources and backgrounds. The most interesting feature is the suppression of the one-point function in the presence of an oscillating source and weak random background. We have also computed analytically and numerically the two-point function in the weak disorder limit. We have found that, in general, the perturbative contribution induces an additional power-law decay whose exponent depends on the distribution of disorder. For certain choices of the gravity background, this contribution becomes dominant for large separations which indicates breaking of perturbation theory and the possible existence of a phase transition induced by disorder.