Spontaneously Generated Inhomogeneous Phases via Holography

TL;DR

This paper presents a holographic model where a higher-derivative interaction induces spontaneous formation of inhomogeneous phases, leading to spatially varying charge densities in the dual gauge theory.

Contribution

It introduces a novel holographic setup with higher-derivative terms that spontaneously generate inhomogeneous phases, expanding understanding of phase transitions in gauge/gravity duality.

Findings

Critical temperature for phase transition calculated.

Spontaneous spatially inhomogeneous charge density observed.

Model demonstrates emergence of inhomogeneous phases via higher-derivative interactions.

Abstract

We discuss a holographic model consisting of a $U(1)$ gauge field and a scalar field coupled to a charged AdS black hole under a spatially homogeneous chemical potential. By turning on a higher-derivative interaction term between the $U(1)$ gauge field and the scalar field, a spatially dependent profile of the scalar field is generated spontaneously. We calculate the critical temperature at which the transition to the inhomogeneous phase occurs for various values of the parameters of the system. We solve the equations of motion below the critical temperature, and show that the dual gauge theory on the boundary spontaneously develops a spatially inhomogeneous charge density.