Séminaire Physique mathématique ICJ
# A many-body Fredholm index for quantum charge transport

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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.

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Nguyen-Viet Dang

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