Holography without translational symmetry

TL;DR

This paper introduces a holographic model using massive gravity to describe strongly interacting quantum systems with broken translational symmetry, capturing key transport properties like conductivity and emergent scaling laws.

Contribution

It proposes a novel holographic framework employing massive gravity to model momentum relaxation without explicit inhomogeneities, aligning with previous lattice results.

Findings

Conductivity exhibits a Drude peak approaching a delta function as massless limit.

Optical conductivity follows an emergent power-law scaling law.

Model reproduces key features of inhomogeneous lattice systems.

Abstract

We propose massive gravity as a holographic framework for describing a class of strongly interacting quantum field theories with broken translational symmetry. Bulk gravitons are assumed to have a Lorentz-breaking mass term as a substitute for spatial inhomogeneities. This breaks momentum-conservation in the boundary field theory. At finite chemical potential, the gravity duals are charged black holes in asymptotically anti-de Sitter spacetime. The conductivity in these systems generally exhibits a Drude peak that approaches a delta function in the massless gravity limit. Furthermore, the optical conductivity shows an emergent scaling law: $|\sigma(\omega)| \approx {A \over \omega^{\alpha}} + B$. This result is consistent with that found earlier by Horowitz, Santos, and Tong who introduced an explicit inhomogeneous lattice into the system.