Scaling of the Holographic AC conductivity for non-Fermi liquids at criticality

TL;DR

This paper investigates the frequency-dependent AC conductivity in a holographic non-Fermi liquid model, revealing regimes with Drude peaks and a universal scaling tail characterized by a critical exponent.

Contribution

It demonstrates the emergence of a universal scaling tail in AC conductivity across different regimes and relates the scaling exponent to critical exponents in holographic models.

Findings

Drude peak appears when dissipation dominates DC conductivity

Scaling tail $\sigma_{AC} o ext{const} imes \omega^m$ is universal

Scaling exponent $m$ is expressed via Lifshitz and conduction critical exponents

Abstract

The frequency dependence of the AC conductivity is studied in a holographic model of a non-fermi liquid that is amenable to both analytical and numerical computation. In the regime that dissipation dominates the DC conductivity, the AC conductivity is described well in the IR by a Drude peak despite the absence of quasiparticles. In the regime where pair-production-like processes dominate the conductivity there is no Drude peak. A scaling tail is found for the AC conductivity that is independent of the charge density and momentum dissipation. Evidence is given that this scaling tail $\sigma_{AC}\sim \omega^m$ appears generically in quantum critical holographic systems and the associated scaling exponent $m$ is calculated in terms of the Lifshitz and conduction critical exponents.