Universal Hall Response in Synthetic Dimensions

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 ${\Delta }_{\mathrm{H}}$ is universal and corresponds to a classical Hall resistivity $R_{\mathrm{H}}=-1/n$ 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.

13 pages, 9 figures