Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model

2025/09/29 by Zijian Song, Song, Zijian, Jian-Hao Zhang +1 · 3 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2509.24179

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-Abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states, where symmetries can be either strong or weak. In particular, we investigate the strong-to-weak spontaneous symmetry breaking (SWSSB) of non-invertible higher-form symmetries in non-Abelian Kitaev's quantum double models under decoherence. We further show that the resulting decohered quantum double mixed states form a locally indistinguishable set, which also constitutes an information convex set. Importantly, we emphasize that the dimension of this convex set equals the ground-state degeneracy of the corresponding pure state, highlighting that the quantum information encoded in the ground-state subspace is degraded into classical information captured by the convex set of decohered density matrices.

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Cited by

• Emergent Universality Class in Dissipative Quantum Systems with Dipole Moment Conservation
• Information dynamics and symmetry breaking in generic monitored ℤ₂-symmetric open quantum systems
• Holographic duality between bulk topological order and boundary mixed-state order

Related

• Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space
• Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective
• Hardness of observing strong-to-weak symmetry breaking
• SymTFT Approach for Mixed States with Non-Invertible Symmetries
• Strong-to-Weak Symmetry Breaking Phases in Steady States of Quantum Operations