Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings

TL;DR

This paper explores bosonic states in two dimensions with stable chiral edge modes, revealing a novel bulk-edge correspondence and connecting it to T-duality in heterotic string theory.

Contribution

It demonstrates that two distinct chiral edge phases can correspond to the same bulk phase, linked through T-duality, and introduces a new perspective on bulk-edge relationships in topological states.

Findings

Two different edge phases with the same bulk phase are identified.

The bulk phases are shown to be stably equivalent despite different edge states.

The work connects topological phases to T-duality in heterotic strings.

Abstract

We consider states of bosons in two dimensions that do not support anyons in the bulk, but nevertheless have stable chiral edge modes that are protected even without any symmetry. Such states must have edge modes with central charge $c=8k$ for integer $k$. While there is a single such state with $c=8$, there are, naively, two such states with $c=16$, corresponding to the two distinct even unimodular lattices in 16 dimensions. However, we show that these two phases are the same in the bulk, which is a consequence of the uniqueness of signature $(8k +n, n)$ even unimodular lattices. The bulk phases are stably equivalent, in a sense that we make precise. However, there are two different phases of the edge corresponding to these two lattices, thereby realizing a novel form of the bulk-edge correspondence. Two distinct fully chiral edge phases are associated with the same bulk phase, which is consistent with the uniqueness of the bulk since the transition between them, which is generically first-order, can occur purely at the edge. Our construction is closely related to $T$-duality of toroidally compactified heterotic strings. We discuss generalizations of these results.