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 wavefunction: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be non-local, and impossible to be determined with any local probe. Here we propose instead 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.
Quantum mechanically driven structural-spin glass in two dimensions at finite temperature
在磁性材料中，自旋有时会冻结成空间无序的玻璃态。玻璃形成液体或结构玻璃经常以三维形式存在。然而，在二维（2D）中，据信自旋玻璃和结构玻璃两者在有限温度下永远不可能存在，因为它们被热波动破坏。利用大规模量子蒙特卡罗模拟，我们发现了一个量子力学驱动的二维玻璃相在有限的温度。我们的平台是一个在挫挫三角晶格上具有量子横场的伊辛自旋模型。通过以下三个步骤来理解本发明的玻璃相是如何形成的。首先，通过几何阻挫和量子涨落的相互作用，部分自旋自发形成反铁磁蜂窝状自旋超结构。然后，键相互作用中的小随机性作为对该超结构的相关扰动而起作用，并将其分解成{ \it域}，使其成为结构玻璃。上层结构的玻璃质反过来又产生了一个随机的磁场，作用于剩余的波动自旋，并将它们冻结。由此形成的域的形状敏感地取决于淬火过程，这是玻璃的特征之一，源自多谷自由能景观。本系统仅由{ \it a single}自旋玻璃自由度组成，其自然不会单独成为结构玻璃，也不会单独成为自旋玻璃。然而，具有这两种性质的玻璃以共存的双组分玻璃、代数结构玻璃和长程有序自旋玻璃的形式出现。这种玻璃形成机制的新概念开辟了一条即使在低维系统中也能实现功能玻璃的途径。
