Symmetry-Protected Topological Interfaces and Entanglement Sequences

TL;DR

This paper explores how gapped interfaces in 2D Abelian topological phases host sequences of 1D symmetry-protected topological states, linking entanglement entropy corrections to these states and their symmetry properties.

Contribution

It introduces the Boundary Topological Entanglement Sequence, connecting entanglement entropy corrections to classes of 1D SPT states at topological interfaces.

Findings

Interfaces support a sequence of 1D SPT states.

Entanglement entropy correction signals SPT emergence.

Domain walls host parafermion-like excitations.

Abstract

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 in Ref.~\onlinecite{cano-2015}. The topological entanglement entropy decomposes as $\gamma = \gamma_a + \gamma_s$, where $\gamma_a > 0$ only depends on universal topological properties of the 2D state, while a correction $\gamma_s > 0$ 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 $\gamma_s$ associated with a given interface - which is named 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.