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arXiv 2601.06010cond-mat.stat-mechquant-ph
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三维 Z₂ 位形场论中的慢混合与涌现的一形式对称性

Slow mixing and emergent one-form symmetries in three-dimensional $\mathbb{Z}_2$ gauge theory

Stanford University（斯坦福大学）；University of Oxford（牛津大学）

Charles Stahl, Benedikt Placke, Vedika Khemani, Yaodong Li

备注：
19+4 pages, 10+1 figures
发表信息：
Phys. Rev. E 114, 034126 (2026)
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AI总结：

研究三维 Z₂ 位形场论中慢混合与涌现的一形式对称性，揭示熵效应在高温下的记忆机制及临界行为。

摘要：

在低温下，对称破缺的顺序通常伴随着缓慢的弛豫动力学，这是由于不同有序态之间的界面导致自由能屏障发散所致。在这里，我们将这种对应关系扩展到经典拓扑序，其中有序态在局部上无法区分，因此不存在它们之间的界面概念。我们研究了三维（3D）经典 Z₂ 位形场论（LGT）的弛豫动力学，作为典型例子。我们证明了在无束缚相中混合时间的下界，t_mix = exp[Ω(L)]，其中 L 是线性系统尺寸。这个下界即使在存在破坏不同长寿命态之间一形式对称性的扰动时也适用。这种扰动破坏了有序态之间的能量屏障，但我们显示在非零温度下，熵效应仍然导致自由能屏障发散。我们的证明确立了 LGT 作为稳健的有限温度经典记忆。我们进一步证明熵效应导致了涌现的一形式对称性，通过我们精确定义的概念。我们论证指数混合时间源于无束缚相的普遍性质，并通过研究从无束缚相中出的 Higgs 和束缚相的混合时间尺度来数值验证这一预期。这些相变显示出明显不同的动态标度，尽管它们都具有 3D 伊辛模型的静态临界指数。我们预期这种新的熵机制对于记忆和涌现对称性的贡献也将为自纠正量子记忆提供见解。

英文摘要：

Symmetry-breaking order at low temperatures is often accompanied by slow relaxation dynamics, due to diverging free-energy barriers arising from interfaces between different ordered states. Here, we extend this correspondence to classical topological order, where the ordered states are locally indistinguishable, so there is no notion of interfaces between them. We study the relaxation dynamics of the three-dimensional (3D) classical $\mathbb{Z}_2$ lattice gauge theory (LGT) as a canonical example. We prove a lower bound on the mixing time in the deconfined phase, $t_{\text{mix}} = \exp [Ω(L)]$, where L is the linear system size. This bound applies even in the presence of perturbations that explicitly break the one-form symmetry between different long-lived states. This perturbation destroys the energy barriers between ordered states, but we show that entropic effects nevertheless lead to diverging free-energy barriers at nonzero temperature. Our proof establishes the LGT as a robust finite-temperature classical memory. We further prove that entropic effects lead to an emergent one-form symmetry, via a notion that we make precise. We argue that the exponential mixing time follows from universal properties of the deconfined phase, and numerically corroborate this expectation by exploring mixing time scales at the Higgs and confinement transitions out of the deconfined phase. These transitions are found to exhibit markedly different dynamic scaling, even though both have the static critical exponents of the 3D Ising model. We expect this novel entropic mechanism for memory and emergent symmetry to also bring insight into self-correcting quantum memories.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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