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。

对强关联体系的计算与理解一直是困扰量子材料、量子化学等领域的重要科学问题。比如费米哈勃模型的计算无法在经典计算机上有效的进行，严格对角化、量子蒙特卡洛、张量网络等方法均做了大量的尝试，但是目前仍无法得到令人满意的结果，而量子模拟对这个问题的解决提供了一种可以借助量子效应加速的方法。针对费米哈勃模型，人们将满足费米统计的原子放在光晶格中进行量子模拟，以期理解高温超导的微观物理机制，从而辅助更高温超导材料的寻找并降低其时间成本。但是目前开展的实验在参杂区间仍无法做到足够低的温度区间，这是光晶格量子模拟领域一个重要的科学难题。..针对这一科学问题，该项目提出了一种量子绝热参杂的方案。方案基于连续可调的非公度光晶格的进行绝热量子模拟，粒子数守恒与周期的可控性结合导致任意费米填充数的费米-哈勃模型都可以通过量子绝热演化达到。研究指出其中原子局域化的核心困难，并利用相互作用的调节得到了一个计算复杂度的量子相变，使得量子模拟的时间效率获得指数加速，解决了局域化带来的效率问题。项目系统详尽的研究了粒子参杂和空穴参杂的联系与区别，理清了多体局域化效应在不同参数区间起到的作用的异同，并通过哈密顿量演化路径设计的方式，引入光晶格中的多体局域化相变，从而起到大大加速费米哈伯德模型量子绝热演化的时间效率。..项目书中设定的光晶格多体局域化研究顺利完成。