Incoherent transport for phases that spontaneously break translations

TL;DR

This paper investigates phases of matter that spontaneously break translation symmetry, deriving new expressions for thermoelectric conductivities and showing how to compute DC conductivity via holographic methods involving horizon fluid dynamics.

Contribution

It introduces a boost invariant incoherent current operator and generalizes thermoelectric conductivity expressions beyond translational invariance, with holographic computations of DC conductivity.

Findings

Incoherent current operator identified without hydrodynamic limit

Generalized thermoelectric conductivities for translation-breaking phases

Holographic DC conductivity obtained from horizon fluid dynamics

Abstract

We consider phases of matter at finite charge density which spontaneously break spatial translations. Without taking a hydrodynamic limit we identify a boost invariant incoherent current operator. We also derive expressions for the small frequency behaviour of the thermoelectric conductivities generalising those that have been derived in a translationally invariant context. Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions.