Universal Hall Response in Synthetic Dimensions

TL;DR

This paper investigates the Hall effect in synthetic multi-leg ladder systems with interactions, revealing a universal Hall response under certain symmetries and interaction-driven phenomena like sign reversal away from those conditions.

Contribution

It identifies a universal regime for the Hall response in interacting synthetic ladder systems and explores how interactions influence this response.

Findings

Universal Hall imbalance $ extstyle riangle_{ m H}$ matches classical Hall resistivity $R_{ m H}=-1/n$

Interaction effects cause sign reversal of the Hall response

Divergence of Hall response occurs away from high symmetry points

Abstract

We theoretically study the Hall effect on interacting $M$-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on $SU(M)$ symmetric interacting bosons and fermions, as relevant for e.g. typical synthetic dimensional quantum gas experiments, we identify an extensive regime in which the Hall imbalance $\Delta_{\rm H}$ is universal and corresponds to a classical Hall resistivity $R_{\rm H}=-1/n$ for a large class of quantum phases. Away from this high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.