Séminaire Physique mathématique ICJ

A many-body Fredholm index for quantum charge transport

by Wojciech De Roeck

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne

We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any gapped systems with topologically ordered, possibly, degenerate ground states and  requires $U(1)$-gauge symmetry. It is fractional with the denominator given by the ground state degeneracy. In the case that this fraction is not an integer, the construction of the index provides a non-trivial braiding and gives an explicit construction of unitary operators that create  fractionally charged Abelian anyons.

Organized by

Nguyen-Viet Dang