Ground-state degeneracy of correlated insulators with edges

Using the topological flux insertion procedure, the ground-state degeneracy of an insulator on a periodic lattice with filling factor = p /q was found to be at least q-fold. Applying the same argument in a lattice with edges, we show that the degeneracy is modified by the additional edge density E associated with the open boundaries. To carry out this generalization we demonstrate how to distinguish between bulk and edge states, and follow how an edge modifies the thermodynamic limit of Oshikawa’s original argument. In particular, we also demonstrate that these edge corrections may even make an insulator with integer bulk filling degenerate.