Frequency-Temperature Crossover in the Conductivity of Disordered Luttinger Liquids

TL;DR

This paper investigates how disorder affects the electrical conductivity of Luttinger liquids, revealing a crossover in behavior with temperature and frequency, and contrasting perturbation theory with renormalization group results.

Contribution

It provides a systematic analysis of conductivity in disordered Luttinger liquids using both perturbation theory and RG, highlighting differences in scaling behaviors.

Findings

Perturbation theory predicts ω/T scaling of conductivity.

RG analysis shows violation of ω/T scaling.

Non-linear field dependence exhibits distinct power-law scaling.

Abstract

The temperature ($T$) and frequency ($\omega$) dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\omega/T$ scaling of the conductivity such scaling is violated in the RG traetment. We also determine the non-linear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.