Ground-State Degeneracy of Correlated Insulators with Edges

Abstract

Using the topological flux insertion procedure, the ground-state degeneracy of an insulator on a periodic lattice with filling factor $ν=p/q$ 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 $ν_{\mysw{E}}$ associated with the open boundaries. In particular, we demonstrate that these edge corrections may even make an insulator with integer bulk filling degenerate.

4 pages, REVTeX 4