Locally equivalent pure gapped fermionic ground states and index theory
Locally equivalent pure gapped fermionic ground states and index theory

Chris Bourne, Nagoya University
Jadwin Hall A06
The HartreeFockBogoliubov approximation of superconducting ground states can be naturally described using Araki's selfdual canonical anticommutation relation (CAR) algebra. Using this framework, we first review the Ktheoretic classification of free fermions with an emphasis on unique gapped ground states. Ideas from index theory and coarse geometry then allow us to refine this procedure to obtain topological obstructions between gapped ground states with a prescribed locality. These methods also give us hints towards approaches to understand topological invariants of more general (possibly interacting) gapped fermionic ground states.