Topological aspects of quantum scars

建议的博士项目位于凝聚态理论和量子科学的研究领域。该项目将调查本征态热化假说(ETH)失败的情况，该假说假设，当通过热力学极限下的少数体可观测来检验时，多体量子系统的一般状态与热态似乎无法区分。尽管有ETH，但反例确实存在，例如可积和多体局域系统，以及重要的量子多体伤痕状态，这是当前一个充满活力的研究领域。学生将参与物质的拓扑相和量子多体伤痕的联系的理论探索。该项目旨在综合凝聚态物理学中两个有影响力的研究领域，这两个领域到目前为止在很大程度上仍然是不同的。通常，拓扑学是多体基态的重要标志，就像晶体中的电子一样。对于基态，拓扑与期望的属性相关联，例如对噪声的恢复能力和无损边缘状态。有趣的是，量子多体SCAR态虽然位于高能热态的连续体中，但也可以表现出类似基态的性质。例如，量子疤痕通常以面积定律纠缠和指数衰减的关联为特征。虽然一些健壮的量子疤痕的例子在文献中是已知的，但它们的稳定性的机制目前还不是很清楚。受疤痕和基态的相似性启发，本项目的主要目标是探索稳定量子疤痕的拓扑机制，并仔细检查它们对噪声的弹性。对于完整的拓扑分类，学生将首先学习Affleck-Kennedy-Lieb-Tasaki(AKLT)量子自旋链的疤痕状态的对称分馏。这项研究可能会为在嘈杂的中型量子设备和未来的量子计算机中保护量子信息带来新的策略。通过开展这个项目，这名学生还将帮助帝国理工学院的量子科学和凝聚态理论小组建立起富有成效的合作伙伴关系。

The proposed Ph.D. project lies in the research area of condensed matter theory and quantum science. The project will investigate situations in which the eigenstate thermalization hypothesis (ETH) fails, which posits that generic states of a many-body quantum system appear indistinguishable from thermal states when examined through few-body observables in the thermodynamic limit. Notwithstanding the ETH, counterexamples do exist, such as integrable and many-body-localized systems, and importantly, quantum many-body scar states, which are currently a vibrant area of research. The student will participate in a theoretical exploration at the nexus of topological phases of matter and quantum many-body scars. The project aims to synthesize two impactful research areas in condensed matter physics that have remained largely distinct until now. Typically, topology serves as a marker for a nontrivial many-body ground state, like that of electrons in a crystal. For ground states, topology is associated with desirable properties such as resilience to noise and lossless edge states. Interestingly, quantum many-body scar states - while situated within a continuum of thermal states at high energies - can also manifest ground state-like properties. E.g., quantum scars usually feature area-law entanglement and exponentially decaying correlations. While some examples of robust quantum scars are known in the literature, the mechanism for their stability is at present not well understood. Inspired by the similarity of scar states and ground states, the primary objective of this project is to explore topological mechanisms for stabilizing quantum scars and to scrutinize their resilience to noise. Towards a full topological classification, the student will first study symmetry fractionalization for the scar states of the Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain. This research could give rise to novel strategies for protecting quantum information in noisy intermediate-scale quantum devices and future quantum computers. By undertaking the project, the student will also help cultivate a productive partnership between the quantum science and condensed matter theory groups at Imperial.