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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Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.
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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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Physical constraints on effective non-Hermitian systems
Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.