Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking

• URL: http://arxiv.org/abs/2605.05288v1
• Date: Wed, 06 May 2026 17:59:53 GMT
• Title: Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking
• Abstract summary: Strong-to-weak spontaneous symmetry breaking is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic.<n>We show that the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature.<n>We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner-Yanase skew information.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Strong-to-weak spontaneous symmetry breaking (SWSSB) is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic. We show that, for continuous symmetries, long-range Rényi-1 correlator, together with a sufficiently rapid approach to its nonzero asymptotic value, forces subsystem charge indefiniteness: the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature. This gives a precise static fluctuation footprint of charge scrambling. We construct examples to show that the implication is conditional and non-reversible: dephased superfluids retain Rényi-1 SWSSB with subextensive charge variance when the Rényi-1 tail is too slow, while sparse fixed-charge projectors have extensive charge variance but no local charge-transfer Rényi-1 order or long-range conditional mutual information. Finally, we introduce a \emph{twist overlap} correlator, which serves as an analogue of charge variance applicable to both discrete and continuous symmetries. This naturally decomposes local block-charge fluctuations into strong- and weak-symmetry channels. We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner--Yanase skew information. Taken together, these results give a unified understanding for distinguishing nonlinear SWSSB order, local charge indefiniteness, and coherent charge fluctuations.

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