Generalized symmetry-protected topological phases in mixed states from gauging dualities

TL;DR

This paper develops a framework to classify and construct mixed-state topological phases with generalized symmetries, such as noninvertible and dipole symmetries, using a gauging duality approach, revealing new intrinsic mixed-state phases.

Contribution

It introduces a gauging correspondence that maps mixed-state phases with generalized symmetries to those with ordinary symmetries, enabling classification of new ASPT phases in (1+1)d.

Findings

Classified a subclass of ASPT phases with non-invertible and dipole symmetries.

Constructed explicit models of intrinsic mixed-state ASPT phases.

Characterized phases via string order parameters and protected edge modes.

Abstract

Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably noninvertible and dipole symmetries--have become powerful organizing principles for exotic quantum phases, yet their implications for mixed states remain less explored. In this work, we bridge these directions through a gauging correspondence between mixed-state phases with generalized symmetries and mixed-state phases with ordinary group symmetries, recasting the classification of noninvertible and dipole ASPT phases into familiar classifications of symmetry breaking and ASPT phases with dual symmetries. Using this approach, we classify and construct a subclass of ASPT phases with non-invertible and dipole symmetries in $(1+1)d$, including phases that are intrinsic to mixed states, and characterize them via string order parameters and protected edge modes.