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Integers in gapped quantum lattice systems

Mathematical Physics & Probability

Speaker: Martin Fraas, Virginia Tech
Location: 3106 MSB
Start time: Thu, May 9 2019, 2:10PM

We propose an index for gapped quantum lattice systems that conserve a U(1)-charge. This index takes rational values and it is therefore stable under perturbations. Our formulation is general, but we show that the index reduces to (i) an index of projections in the non-interacting case, (ii) the filling factor for translational invariant systems, (iii) the quantum Hall conductance in the two-dimensional setting without any additional symmetry. In the case of degenerate ground state space with a local topological order, we show that a non-integer value of the index implies the existence of abelian anyonic excitations.