Topological aspects of quantum scars

点击翻译按钮获取中文摘要

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.