Hall Effect in a Quasi-One-Dimensional System

TL;DR

This paper investigates the Hall effect in weakly coupled one-dimensional chains with Luttinger interactions, revealing a power-law dependence of Hall conductivity on magnetic field influenced by interactions.

Contribution

It develops a perturbation theory for the Hall effect in coupled Luttinger liquids, showing the dependence on magnetic field and interaction strength.

Findings

Hall conductivity exhibits a power-law dependence on magnetic field.

Perturbation theory is valid at sufficiently large magnetic fields.

Interaction strength affects the power-law exponent.

Abstract

We consider the Hall effect in a system of weakly coupled one-dimensional chains with Luttinger interaction within each chain. We construct a perturbation theory in the inter-chain hopping term and find that there is a power law dependence of the Hall conductivity on the magnetic field with an exponent depending on the interaction constant. We show that this perturbation theory becomes valid if the magnetic field is sufficiently large.