Higher-order topological phases protected by non-invertible and subsystem symmetries

TL;DR

This paper extends the concept of higher-order topological phases to include non-invertible symmetries, constructing models that host symmetry-protected corner and hinge modes in various dimensions.

Contribution

It introduces a framework for higher-order SPT phases with non-invertible symmetries and provides explicit models in 2+1, 3+1, and higher dimensions.

Findings

Constructed a 2+1D second-order SPT with corner modes protected by non-invertible symmetry

Generalized to d-th order SPT in d+1 dimensions with protected corner modes

Demonstrated a 3+1D second-order SPT with hinge modes protected by non-invertible symmetry

Abstract

Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order symmetry-protected topological (SPT) phases to include non-invertible symmetries. We construct a concrete model of a second-order SPT phase in $2+1$ dimensions that hosts symmetry-protected corner modes protected by a non-invertible symmetry. This construction is then generalized to a $d^{th}$-order SPT phase in $d+1$ dimensions, featuring similarly protected corner modes. Additionally, we demonstrate a second-order SPT phase in $3+1$ dimensions exhibiting hinge modes protected by a non-invertible symmetry.