Topological Holography for Mixed-State Phases and Phase Transitions

• URL: http://arxiv.org/abs/2507.06218v1
• Date: Tue, 08 Jul 2025 17:51:00 GMT
• Title: Topological Holography for Mixed-State Phases and Phase Transitions
• Authors: Ran Luo, Yi-Nan Wang, Zhen Bi,
• Abstract summary: We extend the symmetry topological field theory (SymTFT) framework to open quantum systems.<n>We study (1+1)-dimensional mixed-state phases through condensable algebras in the SymTFT.<n>We show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.
• Score: 5.6658173165064785
• License: http://creativecommons.org/licenses/by/4.0/
• 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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