发表机构
Zhejiang University; Institute of Physics, Chinese Academy of Sciences（浙江大学; 中国科学院物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究开放量子系统中强到弱对称性破缺序的衰减，发现离散Z2对称性下指数衰减，而连续U(1)对称性下通过电荷扇区展宽导致代数弛豫，并给出严格的代数下界及两阶段动力学标度。
AI 中文摘要
强到弱自发对称性破缺（SW-SSB）是混合量子态的一种独特现象，其特征是与强对称性相关的非线性长程关联。然而，在现实开放量子系统中，强对称性在宏观尺度上是脆弱的，并且可以通过与环境的局域电荷交换被明确地约化为弱对称性。在本文中，我们研究了在强对称性破缺的Liouvillian动力学下，SW-SSB序如何衰减。对于离散的$\mathbb{Z}_2$对称性，局域对称性破缺微扰驱动Rényi-1长程关联函数呈指数衰减，揭示了离散SW-SSB序的脆弱性。相比之下，对于连续的$U(1)$对称性，局域电荷交换使对称性电荷扇区上的分布展宽，并导致参数上更慢的代数弛豫。我们建立了连通Rényi-1长程关联的严格代数下界，证明了这种慢弛豫的鲁棒性。在热力学极限下，我们进一步揭示了两阶段动力学标度：早期$\tilde{R}_1\sim t^{-1}$，长时间$\tilde{R}_1\sim t^{-1/z}$，其中$z$由底层流体动力学动力学决定。作为数值验证，我们考虑了$z=2$和$z=4$的费米子链，与理论预测高度吻合。
英文摘要
Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete $\mathbb{Z}_2$ symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous $U(1)$ symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: $\tilde{R}_1\sim t^{-1}$ at early times and $\tilde{R}_1\sim t^{-1/z}$ at long times, with $z$ set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with $z=2$ and $z=4$, which are excellent agreement with the theoretical predictions.
Comments22 pages, 5 figures
