Hall effect in strongly correlated low dimensional systems

TL;DR

This paper studies the Hall effect in quasi-one-dimensional systems of weakly coupled Luttinger Liquids, revealing temperature and frequency-dependent deviations from free-fermion behavior due to umklapp scattering.

Contribution

It introduces a memory function approach to compute the Hall coefficient in strongly correlated low-dimensional systems, highlighting the impact of Luttinger parameters.

Findings

Hall coefficient exhibits power-law corrections depending on Luttinger parameter

At high temperature or frequency, the Hall coefficient approaches the band value

The study provides a quantitative link between correlations and Hall effect behavior

Abstract

We investigate the Hall effect in a quasi one-dimensional system made of weakly coupled Luttinger Liquids at half filling. Using a memory function approach, we compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter $K_{\rho}$. At high enough temperature or frequency the Hall coefficient approaches the band value.