Local diagnostics for strong-to-weak spontaneous symmetry breaking and non-equilibrium phase transitions
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| Format: | Preprint |
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2026
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| _version_ | 1866917542383058944 |
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| author | Zhang, Carolyn |
| author_facet | Zhang, Carolyn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local diagnostics for strong-to-weak spontaneous symmetry breaking and non-equilibrium phase transitions Zhang, Carolyn Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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. |
| title | Local diagnostics for strong-to-weak spontaneous symmetry breaking and non-equilibrium phase transitions |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.29113 |