Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.
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Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.
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Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.
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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.