Out-of-bounds hydrodynamics in holographic anisotropic Dirac semimetals

TL;DR

This paper models a strongly correlated 2+1D condensed matter system with a thermal phase transition using holography, revealing violations of the KSS-bound and details of quantum critical behavior.

Contribution

It introduces backreaction in holographic models of anisotropic Dirac semimetals, demonstrating KSS-bound violation and analyzing quantum critical points.

Findings

Violation of the KSS-bound for shear viscosity to entropy ratio.

Identification of a quantum critical point at zero temperature.

Lifshitz critical exponent approximately equal to 2.

Abstract

We present a version of a strongly correlated 2+1-dimensional condensed matter system that features a thermal phase transition between a semimetal and an insulator through a semi-Dirac quantum critical region using AdS/CFT holography. We introduce backreaction into the bulk equations of motion to measure transport coefficients in the boundary; specifically the shear viscosity $\eta$. By explicitly breaking rotational symmetry we find a new instance of violation of the KSS-bound for the $\eta/s$ ratio in the quantum critical region, as well as a monotone dependence on temperature in the $T\to 0$ regime fixed by a Lifshitz dynamical critical exponent. We find that the Lifshitz critical exponent in the anisotropic direction is approximately equal to $2$ for our choice of backreaction parameters. We find explicit $T=0$ solutions separated by a quantum critical point in parameter space, showing that the thermal critical phase found in previous work comes from a quantum phase transition at zero temperature.