All Abstracts | Poster Abstracts | Talk Abstracts | Tutorial Abstracts

Proving Hall Conductance Quantization

Matthew Hastings, Microsoft Station Q

(Session 11 : Sunday from 8:30-9:15)

Abstract. Ever since Laughlin's original gauge argument for Hall conductance quantization, mathematicians and physicists have tried to find a general proof. Unfortunately, current approaches either require extra assumptions or are limited to noninteracting electrons. Using quasi-adiabatic continuation, we are able to remove these limitations. I will try to explain how quasi-adiabatic continuation can be used as a general "toolkit": once the machinery is developed, many results follow directly, including this, the higher dimensional Lieb-Schultz-Mattis theorem, Goldstone's theorem, and more. This is joint work with S. Michalakis.