Transport in Luttinger Liquids

TL;DR

This paper analyzes the transport properties of one-dimensional Luttinger liquids, revealing temperature-dependent conductivity behaviors through renormalization group and tunneling calculations, including power-law and exponential dependencies.

Contribution

It introduces a detailed analysis of conductivity in Luttinger liquids using bosonization and instanton methods, providing new insights into low-temperature tunneling effects.

Findings

Conductivity exhibits power-law dependence on temperature at intermediate ranges.

At low temperatures, tunneling dominates, leading to an exponential conductivity decay.

Results align with and extend the variable range hopping model.

Abstract

We compute the transport properties of one dimensional interacting electrons, also known as a Luttinger liquid. We show that a renormalization group study allows to obtain the temperature dependence of the conductivity in an intermediate temperature range. In this range the conductivity has a power-law like dependence in temperature. At low temperatures, the motion proceed by tunnelling between localized configurations. We compute this tunnelling rate using a bosonization representation and an instanton technique. We find a conductivity $\sigma(T) \propto e^{-\beta^{1/2}}$, where $\beta$ is the temperature. We compare this results with the standard variable range hopping (VRH) formula.