Séminaire Physique mathématique ICJ

# A many-body Fredholm index for quantum charge transport

## by Wojciech De Roeck

Europe/Paris
Fokko du Cloux (Institut Camille Jordan)

### Fokko du Cloux

#### Institut Camille Jordan

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

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

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