Hall effect of charge carriers in a correlated system

TL;DR

This paper analyzes the dynamical Hall response in correlated electronic systems using linear response theory, deriving explicit expressions for the Hall constant and confirming a hole-like response in a quantum antiferromagnet.

Contribution

It provides a theoretical framework for calculating the dynamical Hall response in correlated systems and explicitly relates the Hall constant to charge stiffness at zero temperature.

Findings

Derived explicit expression for the d.c. Hall constant at T=0.

Confirmed hole-like Hall response in the t-J model.

Reproduced semiclassical results within the quantum model.

Abstract

The dynamical Hall response in a correlated electronic system is analysed within the linear response theory for tight binding models. At $T=0$ the d.c. Hall constant for a single quasiparticle is expressed explicitly via the charge stiffness, and a semiclassical result is recovered. As expected a hole-like response is found for the mobile hole introduced into a quantum antiferromagnet, as represented by the $t-J$ model.