Quantization of Conductance in Gapped Interacting Systems

© 2018, Springer International Publishing AG, part of Springer Nature. We provide a short proof of the quantization of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of Hastings and Michalakis (Commun Math Phys 334:433–471, 2015), simplified by making the stronger assumption that the Hamiltonian remains gapped when threading the torus with fluxes. We argue why this assumption is very plausible. The conductance is given by Berry’s curvature and our key auxiliary result is that the curvature is asymptotically constant across the torus of fluxes.status: publishe