Duality viewpoint of noninvertible symmetry protected topological phases

TL;DR

This paper uses duality transformations to classify and construct noninvertible symmetry protected topological phases across various dimensions, revealing new phases beyond traditional group symmetry classifications.

Contribution

It introduces a duality-based framework for classifying and constructing noninvertible SPT phases, extending beyond conventional group symmetry approaches.

Findings

New classifications of noninvertible SPT phases in arbitrary dimensions

Explicit lattice models realizing these phases in 1+1D and 2+1D

Analysis of anomalous interfaces in the constructed models

Abstract

Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and construction of gapped phases with noninvertible symmetry can be mapped to those involving conventional group symmetries. We demonstrate this approach by classifying symmetry-protected-topological phases with a broad class of noninvertible symmetries in arbitrary spacetime dimensions. Our results reveal new classifications that extend beyond those based on group symmetries. Additionally, we construct lattice models in $(1+1)D$ and $(2+1)D$ that realize these new phases and explore their anomalous interfaces.