Intrinsic NISPT Phases, igNISPT Phases, and Mixed Anomalies of Non-Invertible Symmetries

TL;DR

This paper introduces a new class of topological phases protected by non-invertible symmetries, including intrinsic NISPT and igNISPT phases, constructed via discrete gauging and anomaly resolution, with concrete lattice models provided.

Contribution

It constructs intrinsic NISPT and igNISPT phases using discrete gauging and anomaly analysis, expanding the understanding of non-invertible symmetry protected topological phases.

Findings

Constructed explicit lattice models for NISPT and igNISPT phases.

Generalized intrinsic NISPT phases to (3+1)-dimensional systems.

Identified mechanisms for anomaly resolution in categorical symmetries.

Abstract

A bosonic non-invertible Symmetry Protected Topological (NISPT) phase in (1+1)-dim is referred to as $\textit{intrinsic}$ if it cannot be mapped, under discrete gauging, to a gapped phase with any invertible symmetry, that is, if it is protected by a non-group-theoretical fusion category symmetry. We construct the intrinsic NISPT phases by performing discrete gauging in a partial SSB phase with a fusion category symmetry that has a certain mixed anomaly. Sometimes, the anomaly of that symmetry category can be alternatively understood as a self-anomaly of a proper categorical sub-symmetry; when this is the case, the same gauging provides an anomaly resolution of this anomalous categorical sub-symmetry. This allows us to construct intrinsic gapless SPT (igSPT) phases, where the anomalous faithfully acting symmetry is non-invertible; and we refer to such igSPT phases as igNISPT phases. We provide two concrete lattice models realizing an intrinsic NISPT phase and an igNISPT phase, respectively. We also generalize the construction of intrinsic NISPT phases to (3+1)-dim.