A many-body Fredholm index for quantum charge transport

par Wojciech De Roeck

vendredi 11 oct. 2019, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Institut Camille Jordan)

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.