Mixed-state phases from local reversibility

TL;DR

This paper introduces a refined definition of mixed-state phase equivalence using locally reversible channels, revealing non-trivial topological features in classical loop ensembles previously considered trivial.

Contribution

It develops a new framework for mixed-state phases based on local reversibility, preserving symmetries and anomalies, and applies it to classical loop models.

Findings

Refined definition preserves topological degeneracy and symmetries.

Classical loop ensemble has non-trivial topological features under the new definition.

Demonstrates that some classical models are non-trivial phases under the refined criteria.

Abstract

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a new generalization of symmetry for open quantum systems. For abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has non-trivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.