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

2025/07/23 by Sheinbaum, Daniel, Camarena, Omar Antolín
#Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2507.17179

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).

Citations

• Weak topological phases in the presence of interactions
• Failure of the Crystalline Equivalence Principle for Weak Free Fermions
• Topological insulators with inversion symmetry

Related

• Mixed Symmetries of SPT Phases
• Failure of the Crystalline Equivalence Principle for Weak Free Fermions
• Disordered topological crystalline phases
• Crystalline equivalent boundary-bulk correspondence of two-dimensional topological phases
• Lattice models with subsystem/weak non-invertible symmetry-protected topological order