Topological aspects of quantum scars

拟申请博士项目研究方向为凝聚态理论与量子科学。该项目将研究特征态热化假设（ETH）失效的情况，该假设假定，在热力学极限下，通过少体观测来检查时，多体量子系统的一般状态与热状态无法区分。尽管如此，反例确实存在，例如可积和多体定域系统，重要的是，量子多体疤痕态，这是目前一个充满活力的研究领域。学生将参与有关物质拓扑相与量子多体伤痕关系的理论探索。该项目旨在综合凝聚态物理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标记，就像晶体中的电子一样。对于基态，拓扑结构与期望的特性有关，如抗噪声和无损边缘状态。有趣的是，量子多体疤痕态——虽然位于高能量的热态连续体中——也可以表现出类似基态的特性。例如，量子伤疤通常具有面积定律纠缠和指数衰减相关性。虽然文献中已知一些强健量子疤痕的例子，但其稳定性的机制目前尚未得到很好的理解。受疤痕态和基态相似性的启发，本项目的主要目标是探索稳定量子疤痕的拓扑机制，并仔细研究它们对噪声的恢复能力。为了实现完整的拓扑分类，学生将首先研究Affleck-Kennedy-Lieb-Tasaki （AKLT）量子自旋链的疤痕态的对称分数化。这项研究可能会产生新的策略来保护嘈杂的中等规模量子设备和未来的量子计算机中的量子信息。通过承担这个项目，学生还将帮助培养帝国理工学院量子科学和凝聚态理论小组之间富有成效的伙伴关系。

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.