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arXiv:2605.29113

Local diagnostics for strong-to-weak spontaneous symmetry breaking and non-equilibrium phase transitions

Carolyn Zhang

quant-phcond-mat.stat-mechcond-mat.str-elSubmitted May 27, 2026• Announced May 29, 2026• 0 citations
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Abstract

We construct strongly $\mathbb{Z}_2$-symmetric local Markov/Lindblad dynamics exhibiting transitions between strong-paramagnetic behavior and strong-to-weak spontaneous symmetry breaking. In 1+1d, an absorbing-state construction gives a transition with scaling consistent with the parity-conserving branching-annihilating random-walk universality class. In 2+1d, a pair-flip variant of Toom's rule provides evidence for a stable strong-paramagnetic/weakly symmetry-broken regime and a transition into an active SWSSB regime. We also introduce a marginal fidelity correlator of radius $R$, a local proxy for the usual SWSSB fidelity order parameter requiring tomography only on $\mathcal{O}(R^d)$-size regions. For broad classes of states, including symmetry-projected Gibbs-like states satisfying suitable local indistinguishability assumptions, we bound the error between the marginal and global fidelity correlators by terms decaying exponentially in $R$. These marginal fidelities provide a model-independent diagnostic of SWSSB in absorbing-state transitions, where microscopic notions of defects or activity are not universal.

Comments
5.5 pages with 3 figures in the main text, 10 pages of supplemental material including 3 figures

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