论文标题
相互作用的二维晶格理论中无序的定位
Disorder-free localization in an interacting two-dimensional lattice gauge theory
论文作者
论文摘要
最近引入了无障碍定位作为一种机制，用于在低维质量晶格量规理论中破裂的机制，这是由量规不变性施加的局部约束引起的。我们表明，在两个空间维度上的真正相互作用的系统也可能由于这种机制而变得非效应。具体而言，我们通过通过经典的相关渗透问题获得了量子链路模型中的非效应行为，这意味着在过渡的非迫切一侧，这意味着希尔伯特空间的碎片。我们通过类似于人工神经网络的经典旋转的变异网络来研究该系统中的量子动力学。我们通过研究线缺陷的传播来确定一个明显的动态特征，分别在局部和厄贡阶段产生不同的光锥结构。我们在这项工作中介绍的方法可以应用于任何具有有限尺寸的局部希尔伯特空间的晶格量规理论，而与空间维度无关。
Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. Specifically, we prove nonergodic behavior in the quantum link model by obtaining a rigorous bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by means of an efficient and perturbatively controlled representation of the wavefunction in terms of a variational network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.
