Hall response in interacting bosonic and fermionic ladders

TL;DR

This paper analyzes the Hall response in interacting bosonic and fermionic two-leg ladders threaded by flux, deriving explicit expressions and identifying phase-dependent behaviors using bosonization with band curvature effects.

Contribution

It introduces a perturbative approach to compute the Hall imbalance including interactions and distinguishes phases via flux dependence.

Findings

Hall imbalance varies with flux, distinguishing phases

Universal behavior in Galilean invariant systems

Relation between Hall resistance and charge stiffness

Abstract

We use bosonization, retaining band curvature terms, to analyze the Hall response of interacting bosonic and fermionic two-leg ladders threaded by a flux. We derive an explicit expression of the Hall imbalance in a perturbative expansion in the band curvature, retaining fully the interactions. We show that the flux dependence of the Hall imbalance allows to distinguish the two phases (Meissner and Vortex) that are present for a bosonic ladder. For small magnetic field we relate the Hall resistance, both for bosonic and fermionic ladders, to the density dependence of the charge sitffness of the system in absence of flux. Our expression unveil a universal interaction-independent behavior in the Galilean invariant case.