The gravity dual to a quantum critical point with spontaneous symmetry breaking

TL;DR

This paper explores gravity duals of quantum critical points with spontaneous symmetry breaking, revealing unique infrared behaviors and power-law scalings in transport properties within a holographic framework.

Contribution

It constructs zero temperature gravity solutions with dual quantum critical points exhibiting spontaneous symmetry breaking and unusual infrared scaling behaviors.

Findings

Infrared geometry contains two AdS regions with different conformal invariance

The effective signal speed is reduced in the infrared region

Conductivity exhibits power-law scaling, approximately as omega^3.5 at low frequencies

Abstract

We consider zero temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant. With appropriate choices of parameters, the geometry contains two copies of anti-de Sitter space, one describing conformal invariance in the ultraviolet, and one in the infrared. The effective speed of signal propagation is smaller in the infrared. Green's functions and associated transport coefficients can have unusual power law scaling in the infrared. We provide an example in which the real part of the conductivity scales approximately as omega^3.5 for small omega.