Holographic geometries for condensed matter applications

TL;DR

This paper explores holographic geometries derived from Einstein-Dilaton-Maxwell theory to model strongly correlated condensed matter systems, analyzing their spacetime symmetries, entanglement entropy, and low-energy phenomena.

Contribution

It introduces novel spacetime geometries with Lifshitz scaling and hyperscaling violation, connecting holographic models to condensed matter phenomena.

Findings

Planar black brane solutions exhibit Lifshitz scaling.

Entanglement entropy and Wilson loops analyzed via minimal surfaces.

Coupling to matter fields induces U(1) symmetry breaking and emergent scaling.

Abstract

Holographic modeling of strongly correlated many-body systems motivates the study of novel spacetime geometries where the scaling behavior of quantum critical systems is encoded into spacetime symmetries. Einstein-Dilaton-Maxwell theory has planar black brane solutions that exhibit Lifshitz scaling and in some cases hyperscaling violation. Entanglement entropy and Wilson loops in the dual field theory are studied by inserting simple geometric probes involving minimal surfaces into the black brane geometry. Coupling to background matter fields leads to interesting low-energy behavior in holographic models, such as U(1) symmetry breaking and emergent Lifshitz scaling.