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arXiv · 2507.06218

Topological Holography for Mixed-State Phases and Phase Transitions

Ran Luo·Yi-Nan Wang·Zhen Bi
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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.

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Ran Luo, Yi-Nan Wang, Zhen Bi. 2025-07-08. Topological Holography for Mixed-State Phases and Phase Transitions. https://arxiv.org/abs/2507.06218

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