The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.

中文翻译：

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量子多体疤痕和希尔伯特空间碎片：精确结果回顾


里德堡原子模拟器和 Affleck-Kennedy-Lieb-Tasaki spin-1 链模型中量子多体疤痕 (QMBS) 的发现表明，对遍历性的弱违反仍然可以带来丰富的实验和理论物理。在这篇综述中，我们借助费米子哈伯德模型等简单示例，对孤立量子系统中 QMBS 弱遍历性破坏的确切结果进行了教学介绍和概述。我们还讨论了各种机制和统一的形式体系，这些机制和形式体系已被提议涵盖众多展示 QMBS 的系统。我们介绍了导致特定初始状态精确复兴的等距塔的示例，以及 QMBS 的孤立示例。最后，我们回顾了希尔伯特空间碎片，这是一种相关现象，系统表现出更丰富的遍历和非遍历行为，并讨论了它与 QMBS 的联系。