Topological aspects of quantum scars

量子疤痕的拓扑方面

• 批准号: 2892181
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2892181
• 关键词: Topological; aspects; quantum; scars

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.

建议的PhD该项目的研究领域是凝聚态理论和量子科学。该项目将调查本征态热化假设（ETH）失败的情况，该假设假定多体量子系统的一般状态在通过热力学极限中的少体观测量进行检查时与热态无法区分。尽管有ETH，但反例确实存在，例如可积和多体局域系统，重要的是，量子多体疤痕状态，这是目前一个充满活力的研究领域。学生将参与在物质和量子多体伤疤的拓扑相的关系的理论探索。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，这两个领域迄今为止在很大程度上保持着不同。通常，拓扑结构是一个非平凡的多体基态的标记，就像晶体中的电子一样。对于基态，拓扑结构与期望的属性相关联，例如对噪声的弹性和无损边缘状态。有趣的是，量子多体疤痕态--虽然位于高能热态的连续体中--也可以表现出基态的性质。例如，在一个示例中，量子疤痕通常以面积定律纠缠和指数衰减相关为特征。虽然在文献中已知一些稳健的量子疤痕的例子，但其稳定性的机制目前还没有很好地理解。受疤痕状态和基态的相似性的启发，该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。为了达到完整的拓扑分类，学生将首先研究阿弗莱克-肯尼迪-利布-田崎（AKLT）量子自旋链的疤痕状态的对称性分解。这项研究可能会产生新的策略，用于保护噪声中等规模量子设备和未来量子计算机中的量子信息。通过开展该项目，学生还将有助于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。