Mixed-state Phases from Higher-order SSPTs with Kramers-Wannier Symmetry

TL;DR

This paper explores mixed-state phases derived from higher-order subsystem SPT phases with Kramers-Wannier symmetry, revealing coexistence of topological order and symmetry breaking, and characterizing phase distinctions via interfaces.

Contribution

It introduces a study of mixed states from higher-order subsystem SPT phases protected by non-invertible symmetries, highlighting their complex phase coexistence and interface properties.

Findings

Mixed states show coexistence of SPT order and SWSSB.

Interfaces can distinguish different phases when symmetries are preserved.

Mixed states exhibit unique phase behaviors from higher-order SSPTs.

Abstract

Mixed-state phases have recently attracted significant attention as a generalization beyond their pure-state counterparts. Prominent examples include mixed-state symmetry-protected topological (mSPT) phases and the strong-to-weak symmetry breaking (SWSSB) phases. It has been shown recently that mSPT phases admit a holographic dual description in terms of higher-order subsystem SPT phases. In this work, we investigate the mixed-state phases obtained by tracing out the bulk degrees of freedom of higher-order subsystem SPT phases protected by non-invertible symmetries. We find that the resulting mixed states exhibit the coexistence of the symmetry-protected topological order and SWSSB. We also use the interface as a probe to characterize the mixed state phases, and specifically, when there is no local modification to preserve the symmetries across the interface, the two sides of the interface are in distinct phases.