Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems
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| Format: | Preprint |
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2026
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| _version_ | 1866914475021434880 |
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| author | Shu, Chang Zhang, Kai Luo, Zhu-Xi You, Yizhi Sun, Kai |
| author_facet | Shu, Chang Zhang, Kai Luo, Zhu-Xi You, Yizhi Sun, Kai |
| contents | Strong-to-weak spontaneous symmetry breaking (SWSSB) defines a mixed-state phase of matter--without a pure-state counterpart--in which nonlinear observables such as the Rényi-2 correlator develop long-range order while conventional linear correlations remain short-ranged. Here we study the emergence of SWSSB in one-dimensional open quantum systems governed by Lindbladian evolution, where the transition time diverges with system size and SWSSB appears only asymptotically in the steady state. By tracking the late-time growth of the Rényi-2 correlation length, we uncover a universal dynamical regime controlled purely by the symmetry class of the Lindbladian. Contrary to the conventional expectation that late-time dynamics are governed by the low-lying Liouvillian spectrum, we find that the time dependence of the SWSSB transition--exponential versus algebraic--is dictated solely by symmetry, independent of details of the Lindbladian, including whether the Liouvillian spectrum is gapped or gapless. For $\mathbb{Z}_2$-symmetric dynamics, the Rényi-2 correlation length grows exponentially in time--even when the spectrum is gapless--yielding an effective transition time $t_c \propto \operatorname{ln} L$ and enabling rapid preparation of the $\mathbb{Z}_2$ SWSSB steady state. In contrast, U(1)-symmetric dynamics exhibit algebraic scaling, $t_c \propto L^α$, with a filling-dependent dynamical exponent: ballistic growth ($α\approx 1$) at finite filling crosses over to diffusive scaling ($α= 2$) in the zero-filling limit. These results establish symmetry--rather than spectral gap structure--as the controlling principle for SWSSB late-time dynamical scaling, and open a new route to nonequilibrium symmetry breaking in open quantum systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06363 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems Shu, Chang Zhang, Kai Luo, Zhu-Xi You, Yizhi Sun, Kai Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics Strong-to-weak spontaneous symmetry breaking (SWSSB) defines a mixed-state phase of matter--without a pure-state counterpart--in which nonlinear observables such as the Rényi-2 correlator develop long-range order while conventional linear correlations remain short-ranged. Here we study the emergence of SWSSB in one-dimensional open quantum systems governed by Lindbladian evolution, where the transition time diverges with system size and SWSSB appears only asymptotically in the steady state. By tracking the late-time growth of the Rényi-2 correlation length, we uncover a universal dynamical regime controlled purely by the symmetry class of the Lindbladian. Contrary to the conventional expectation that late-time dynamics are governed by the low-lying Liouvillian spectrum, we find that the time dependence of the SWSSB transition--exponential versus algebraic--is dictated solely by symmetry, independent of details of the Lindbladian, including whether the Liouvillian spectrum is gapped or gapless. For $\mathbb{Z}_2$-symmetric dynamics, the Rényi-2 correlation length grows exponentially in time--even when the spectrum is gapless--yielding an effective transition time $t_c \propto \operatorname{ln} L$ and enabling rapid preparation of the $\mathbb{Z}_2$ SWSSB steady state. In contrast, U(1)-symmetric dynamics exhibit algebraic scaling, $t_c \propto L^α$, with a filling-dependent dynamical exponent: ballistic growth ($α\approx 1$) at finite filling crosses over to diffusive scaling ($α= 2$) in the zero-filling limit. These results establish symmetry--rather than spectral gap structure--as the controlling principle for SWSSB late-time dynamical scaling, and open a new route to nonequilibrium symmetry breaking in open quantum systems. |
| title | Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2603.06363 |