We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

中文翻译：

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多体定位、拓扑和对称

我们回顾了孤立系统中物质的非平衡拓扑状态研究的最新进展。多体局域化现象通常由一些孤立系统在淬灭无序的情况下表现出来，阻止系统平衡到热状态，在这种状态下，拓扑有序所需的微妙量子相关性经常被冲刷掉。相反，多体局域系统可以表现出一种本征态相结构，其中它们的整个多体谱以各种类型的量子阶为特征，通常仅限于量子基态。在介绍了多体定位并解释了它如何保护量子秩序之后，