Weak in the boundary: How weak SPT phases spoil anomaly matching

TL;DR

This paper reveals that weak SPT phases on systems with boundaries do not correspond directly to those on fully periodic systems, challenging the conventional understanding of anomaly inflow and impacting the crystalline equivalence principle.

Contribution

It demonstrates the breakdown of the boundary-bulk correspondence for weak SPT phases and discusses the implications for the crystalline equivalence principle.

Findings

Weak SPT phases on systems with boundaries are not in 1-to-1 correspondence with those on periodic systems.

The standard anomaly inflow interpretation of SPT phases is challenged.

Implications for the crystalline equivalence principle are discussed.

Abstract

We show how weak symmetry protected topological (SPT) phases on systems with a boundary are not in 1-to-1 correspondence with weak SPT phases on fully periodic systems, breaking the standard anomaly inflow interpretation of SPT phases. We further discuss the implications for the crystalline equivalence principle (CEP).