Thermal conductivity at a disordered quantum critical point

TL;DR

This paper investigates thermal conductivity at disordered quantum critical points using holography, revealing universal behaviors, scale invariance, and novel fixed points without employing the replica trick.

Contribution

It identifies new disordered fixed points via relevant deformations of holographic CFTs and characterizes their thermal transport properties in 1+1 dimensions.

Findings

Thermal conductivity approaches a constant at low T in one fixed point class.

In another class, thermal conductivity scales as T^{0.3}.

Thermal conductivity shows discrete scale invariance with logarithmic oscillations.

Abstract

Strongly disordered and strongly interacting quantum critical points are difficult to access with conventional field theoretic methods. They are, however, both experimentally important and theoretically interesting. In particular, they are expected to realize universal incoherent transport. Such disordered quantum critical theories have recently been constructed holographically by deforming a CFT by marginally relevant disorder. In this paper we find additional disordered fixed points via relevant disordered deformations of a holographic CFT. Using recently developed methods in holographic transport, we characterize the thermal conductivity in both sets of theories in 1+1 dimensions. The thermal conductivity is found to tend to a constant at low temperatures in one class of fixed points, and to scale as $T^{0.3}$ in the other. Furthermore, in all cases the thermal conductivity exhibits discrete scale invariance, with logarithmic in temperature oscillations superimposed on the low temperature scaling behavior. At no point do we use the replica trick.