北京大学

摘要：

The disordered quantum systems host three basic types of quantum states, the extended, localized, and critical, which bring up a number of distinct fundamental phases, including the pure phases and coexisting ones with mobility edges. The quantum phases involving critical states are of exceptional interests, but are much less studied compared with the other ones. In this talk, I will present a systematic study of all the fundamental quantum phases in quasiperiodic systems, with a unified framework being established. We start with a class of exactly solvable models, dubbed quasiperiodic mosaic lattice models, hosting novel types of exact mobility edges separating localized from quantum critical or extended states. With these exactly solvable models, we discover a universal mechanism for the critical states that such states are due to the vanishing Lyapunov exponent and the incommensurately distributed hopping zeros in the thermodynamic limit, which also serve as a rigorous characterization of the critical states. We then extend the mechanism of the critical states to a broad regime, in which we predict the existence of seven fundamental phases in a spin-orbit coupled quasiperiodic optical Raman lattices. Further, through the analytic methods including the Avila global theory and renormalization group, various universal results are obtained and provide a rigorous and generic characterization of the different fundamental localization phases. In particular, a generalized universal mechanism for critical states is uncovered. Finally, we show that in the presence of interactions, the critical states turn into the many-body counterparts upon the finite-size scaling analysis, giving a many-body critical phase, which is an exotic phase in-between the thermal phase and many-body localization. We also discuss our latest experimental realization of the present predictions. Future important issues will be commented.

报告人简介：

刘雄军教授2011年博士毕业于德州A&M大学物理系，并在马里兰大学、香港科大高等研究院和麻省理工学院物理系从事博士后研究。2014年9月加入北大量子材料中心。2018年7月获长聘，2019年2月晋升正教授、北大博雅特聘教授。他长期从事冷原子物理和凝聚态理论研究，关注冷原子量子模拟，拓扑超导和拓扑量子计算、量子热化及多体局域化、和关联拓扑体系等。获得国家杰青资助（2018）和二期延续资助（2024）。获得2019年亚太物理学会杨振宁奖（Chen-Ning Yang Award）、2023年中国物理学会周培源物理奖，2024年全球华人物理学会和天文学会亚洲成就奖（Robert T. Poe Prize）等。

地点：M830

联系人：崔晓玲（82648018）