开放量子系统中强到弱自发对称破缺的普遍动力学标度
Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems
AI总结：
研究开放量子系统中强到弱自发对称破缺的出现，发现对称性决定动力学标度而非谱隙结构，揭示了不同对称性下相关长度的指数或幂律增长。
摘要：
强到弱自发对称破缺（SWSSB）定义了一种无纯态对应物的混合态物质相，在其中非线性可观测量如Rényi-2相关子发展出长程有序，而常规线性相关性保持短程。本文研究了一维开放量子系统中SWSSB的出现，其中过渡时间随系统尺寸发散，SWSSB仅在稳态中渐近出现。通过追踪Rényi-2相关长度的晚期时间增长，发现由Lindbladian对称性控制的普遍动力学区域。与传统预期不同，发现SWSSB过渡的时间依赖性（指数 vs 幂律）仅由对称性决定，与Lindbladian细节无关，包括Liouvillian谱是否带隙。对于Z2对称动力学，Rényi-2相关长度随时间指数增长，即使谱是无隙的，产生有效的过渡时间t_c ∝ ln L，允许快速准备Z2 SWSSB稳态。相反，U(1)对称动力学表现出幂律缩放，t_c ∝ L^α，具有依赖填充的动态指数：有限填充时的球形增长（α≈1）在零填充极限下过渡到扩散缩放（α=2）。这些结果确立了对称性而非谱隙结构作为SWSSB晚期动力学缩放的控制原理，并为开放量子系统中的非平衡对称破缺开辟了新途径。
英文摘要：
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.
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