Topological Holography for Mixed-State Phases and Phase Transitions

TL;DR

This paper extends topological field theory methods to classify and analyze mixed-state phases and phase transitions in open quantum systems using a doubled topological order framework.

Contribution

It introduces a systematic classification scheme for mixed-state phases via the open SymTFT and explores phase transitions and phase connections within this framework.

Findings

Classified mixed-state phases including SWSSB and ASPT.

Demonstrated phase transitions involving SWSSB.

Connected different phases through gauging in the open SymTFT.

Abstract

We extend the symmetry topological field theory (SymTFT) framework to open quantum systems. Using canonical purification, we embed mixed states into a doubled (2+1)-dimensional topological order and employ the slab construction to study (1+1)-dimensional mixed-state phases through condensable algebras in the doubled SymTFT. Hermiticity and positivity of the density matrix impose additional constraints on allowable anyon condensations, enabling a systematic classification of mixed-state phases - including strong-to-weak symmetry breaking (SWSSB) and average symmetry-protected topological (ASPT) phases. We present examples of mixed-state phase transitions involving SWSSB and show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.