Ground-State Degeneracy of Correlated Insulators with Edges

TL;DR

This paper investigates how edge effects alter the ground-state degeneracy of correlated insulators, revealing that edges can induce degeneracy even in insulators with integer bulk filling.

Contribution

It extends the topological flux insertion method to systems with edges, showing edge density influences ground-state degeneracy.

Findings

Edge density modifies degeneracy in insulators with edges.

Integer bulk filling insulators can become degenerate due to edge effects.

Edge corrections can induce degeneracy in otherwise non-degenerate insulators.

Abstract

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