Universal Hall Response in Interacting Quantum Systems.

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 Δ_{H} is universal and corresponds to a classical Hall resistivity R_{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.