Quantization of the Hall Conductance for General, Multiparticle Schrödinger Hamiltonians

Abstract

We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schr\"odinger operators with general background potentials. The quantization is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class. This generalizes ideas of Thouless et al., for noninteracting Bloch Hamiltonians to general (interacting and nonperiodic) ones.