超冷原子在光晶格中的多体局域化---从建模分析到新量子相

Anderson localization, recently generalized to many-body localization in interacting systems, is one of the most fascinating quantum phenomena which plays a fundamental role in understanding the breakdown of thermalization in disordered systems. In conventional solid-state materials, the disorder degrees of freedom are typically uncontrollable, which narrows the scope of previous theoretical considerations of localization phenomena. Recent optical lattice experiments in the context of many-body localization has achieved full control of disorders, which opens up new angles and regimes to investigate the fundamental localization theory. For example, in disorder optical lattices, the disorder potential can be made comparable with the lattice confinement, rendering the standard tight-binding treatment invalid. A more intriguing aspect on a fundamental level is that even the microscopic symmetries of the disorder are highly adjustable with the local addressability in optical lattices. These developments inspire new theoretical questions that demand to be addressed: a) continuous disordered systems beyond tight-binding theories and b) the interplay of controllable symmetries and localization. For a), although one can do brute-force numeric calculations, the challenge is to reach large systems due to the computational complexity. To solve this problem, this project intends to combine Wegner flow approach and exact diagonalization, which will substantially reduce the numerical complexity and allow us to tackle thermodynamic-limit systems. For b) this project shall carry out the numeric study and effective field theory analysis. Novel phenomena such as point group symmetry enriched localized phases should be anticipated. This project is expected to deepen our understanding of Anderson, as well as many-body, localization beyond the conventional framework.

安德森局域化在无序系统的量子输运问题中扮演重要角色，近年来被推广到相互作用体系，即多体局域化。在固体系统中，无序自由度一般不可操控，这限制了之前局域化理论的研究视角。近年来无序光晶格的发展实现了对无序的调控，为局域化的理论研究提供了新视野和新思路。比如在无序光晶格中无序强度可以和晶格约束匹配，导致紧束缚模型的失效。从基础研究的角度更有趣的是甚至无序的微观对称性都是可控制的。实验上的进展启发了新的亟需解决的理论问题：a） 连续无序系统中超出紧束缚模型的新物理；b）可控对称性对局域化的影响。对于a），虽然可以做“简单粗暴”的数值计算，但是由于计算复杂度的原因这样能处理的系统非常有限。申请人将结合Wegner Flow和精确对角化的方法解决这一问题。对于b），申请人将利用数值计算和有效场论的方法，研究对称性富化的量子局域状态，并探索在量子计算中的前沿应用。预期该项目将极大的拓展多体局域化的理论。