Analysis Seminar: Martin Fraas (Virginia) "A many-body index for quantum charge transport"

Wed, 02/01/201912:00-13:00
Ross building, room 70
Title: A many-body index for quantum charge transport
Abstract: We propose an index for pairs of a unitary map and a clustering state on many-body quantum systems. We require the map to conserve an integer-valued charge and to leave the state invariant. This index is integer-valued and stable under perturbations. In general, the index measures the charge transport across a fiducial line. We show that it reduces to (i) an index of projections in the case of non-interacting fermions, (ii) the charge density for translational invariant systems, and (iii) the quantum Hall conductance in the two-dimensional setting without any additional symmetry. Example (ii) recovers the Lieb-Schultz-Mattis theorem, and (iii) provides a new and short proof of quantization of Hall conductivity in interacting many body systems.