Symmetry-protected topological interfaces and entanglement sequences

Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical interpretation for the corrections to the topological entanglement entropy of a 2D state with Abelian topological order found by J. Cano, T. L. Hughes, and M. Mulligan [Phys. Rev. B 92, 075104 (2015)10.1103/PhysRevB.92.075104]. The topological entanglement entropy decomposes as γ=γa+γs, where γa>0 only depends on universal topological properties of the 2D state, while a correction γs>0 signals the emergence of the 1D SPT state that is produced by interactions along the entanglement cut and provides a direct measure of the stabilizing symmetry of the resulting SPT state. A correspondence is established between the possible values of γs associated with a given interface - which is named the "boundary topological entanglement sequence" - and classes of 1D SPT states. We show that symmetry-preserving domain walls along such 1D interfaces (or boundaries) generally host localized parafermion-like excitations that are stable to local symmetry-preserving perturbations.