Perturbatively charged holographic disorder

TL;DR

This paper develops a holographic model of perturbatively charged disorder in four-dimensional spacetime, addressing divergences in the geometry and calculating the disorder-averaged DC conductivity with corrections to the AdS baseline.

Contribution

It introduces a perturbative approach to model charged disorder holographically, resolving interior divergences and computing conductivity corrections.

Findings

Disorder-averaged geometry exhibits divergences that can be regularized.

Second-order correction to DC conductivity scales inversely with characteristic disorder scale.

Method extends to systems with finite initial charge density.

Abstract

Within the framework of holography applied to condensed matter physics, we study a model of perturbatively charged disorder in D=4 dimensions. Starting from initially uncharged AdS_4, a randomly fluctuating boundary chemical potential is introduced by turning on a bulk gauge field parameterized by a disorder strength and a characteristic scale k_0. Accounting for gravitational backreaction, we construct an asymptotically AdS solution perturbatively in the disorder strength. The disorder averaged geometry displays unphysical divergences in the deep interior. We explain how to remove these divergences and arrive at a well behaved solution. The disorder averaged DC conductivity is calculated and is found to contain a correction to the AdS result. The correction appears at second order in the disorder strength and scales inversely with k_0. We discuss the extension to a system with a finite initial charge density. The disorder averaged DC conductivity may be calculated by adopting a technique developed for holographic lattices.