Striped Order in AdS/CFT

TL;DR

This paper investigates the spontaneous formation of striped, inhomogeneous phases in a holographic model, revealing a second order phase transition characterized by modulated charge densities and geometrical features in the bulk near zero temperature.

Contribution

It demonstrates the emergence of striped order in the Einstein-Maxwell-axion system and characterizes the phase transition and geometric properties of the bulk and boundary.

Findings

Stripe formation occurs below a critical temperature.

A second order phase transition to inhomogeneous phases is observed.

The stripe width increases and saturates as temperature approaches zero.

Abstract

We study the formation of inhomogeneous order in the Einstein-Maxwell-axion system, dual to a 2+1 dimensional field theory that exhibits a spontaneously generated current density, momentum density and modulated scalar operator. Below the critical temperature, the Reissner-Nordstrom-AdS black hole becomes unstable and stripes form in the bulk and on the boundary. The bulk geometry possesses striking geometrical features, including a modulated horizon that tends to pinch off as T -> 0. On a domain of fixed length, we find a second order phase transition to the striped solution in each of the grand canonical, canonical and microcanonical ensembles, with modulated charges that grow and saturate as we lower the temperature and descend into the inhomogeneous phase. For the black hole on an infinite domain, a similar second order transition occurs, and the width of the dominant stripe increases in the zero temperature limit.