Universal Hall Response in Interacting Quantum Systems

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 SUoMthorn 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(H) is universal and corresponds to a classical Hall resistivity R-H = -1/n for a large class of quantum phases. Away fromthis high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.