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Quantum mechanical and information theoretic view on classical glass transitions

机译：经典玻璃化转变的量子力学和信息理论视图

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摘要

Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition in the latter. At the dynamical level, the transition corresponds to a collapse of the excitation spectrum at a critical point. At the static level, the transition affects the ground-state wave function: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be nonlocal and impossible to be determined with any local probe. Here we instead propose to use concepts from quantum information theory that are not centered around local order parameters, such as fidelity and entanglement measures. We show that for systems derived from the mapping of classical stochastic dynamics, singularities in the fidelity susceptibility translate directly into singularities in the heat capacity of the classical system. In classical glassy systems with an extensive number of metastable states, we find that the prefactor of the area law term in the entanglement entropy jumps across the transition. We also discuss how entanglement measures can be used to detect a growing correlation length that diverges at the transition. Finally, we illustrate how static order can be hidden in systems with a macroscopically large number of degenerate equilibrium states by constructing a three-dimensional lattice gauge model with only short-range interactions but with a finite temperature continuous phase transition into a massively degenerate phase.
机译：使用经典随机动力学的Fokker-Planck描述到量子哈密顿量的映射，我们认为前者的动态玻璃化转变必须在后者的量子相变方面具有精确的定义。在动力学水平上，跃迁对应于激发光谱在临界点处的坍塌。在静态水平上，过渡会影响基态波函数：虽然在某些情况下可以由本地操作员的期望值来获取，但在其他情况下，该顺序可能是非本地的，无法用任何本地探针确定。在这里，我们建议使用量子信息论中不以局部有序参数为中心的概念，例如保真度和纠缠度。我们表明，对于从经典随机动力学映射得出的系统，保真度敏感性中的奇点直接转化为经典系统热容量中的奇点。在具有大量亚稳态的经典玻璃态系统中，我们发现纠缠熵中面积定律项的先验因子跨跃迁跃迁。我们还讨论了纠缠措施如何用于检测在过渡处逐渐增大的相关长度。最后，我们通过构造仅具有短程相互作用但具有有限温度连续相转变为大量简并相的三维晶格规模型，来说明在宏观上具有大量简并平衡状态的系统中如何隐藏静态定序。

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