量子杂质模型的精确计算方法及其在多量子点系统中的应用

Some basic strongly correlated models, such as the Anderson model and Hubbard model, are closely related to quantum impurity models. Thus, it is a key issue for strongly correlated theory to solve quantum impurity models in a universal sense. Although some numerical approaches, such as numerical renormalization group, are widely used, they are restricted by size, temperature or other parameters. Seeking universal and efficient approaches to solve general quantum impurity models is still highly required in strongly correlated physics. In addition, with the technical development of quantum dots, applying quantum impurity models to investigate the physics processes in quantum dots has proved to be of theoretical significance and practical value as well. In this project, we will address the aforementioned key issue by developing a non-perturbative approach to solve quantum impurity models, basing on fundamental equations of quantum mechanics and quantum statistical mechanics. It will be of some advantages, such as non-perturbative system-reservoir interaction treatment and little parameters (temperature, interaction strength) limitation. By using this method, we will systematically study the multiple quantum dots systems, focusing on the physics of two-channel Kondo effect and non-Fermi-liquid behaviors in quantum triple dots. Our work can promote the fundamental research of the strongly correlated theory, on one hand, and provide the theoretical foundation for the application of quantum dots in quantum computation and manipulation, on the other hand.

精确求解量子杂质模型是强关联理论的一个关键所在，也是定量研究量子点尤其是多量子点系统的必要途径。虽然目前已经存在数值重整化群等计算方法，但受体系尺寸及其它参数的限制，无法满足普适高效的要求。本项目立足上述关键问题，首先拟在前期工作基础上，发展并完善求解量子杂质模型的非微扰方法，使其不依赖于哈密顿量的具体形式也不受温度及相互作用强度等参数的限制，从而满足普适高效的要求。然后我们拟运用该方法，将前期多量子点中的Kondo物理的研究工作系统化和深入化，并着重定量研究耦合三量子点中双通道Kondo效应和非Fermi液体行为等前沿问题，以指导实验观测和研究。我们的工作一方面可以推动强关联领域的基础研究；另一方面可以为量子点在量子计算和量子调控中的应用奠定理论基础。

本项目基于密度矩阵的级联运动方程组和量子开放体系的线性响应理论，自主发展了一套精确求解量子杂质模型的非微扰计算方法，该方法普适高效，并且不依赖于温度和相互作用强度等参数。. 运用上述非微扰方法，本项目系统研究了多量子点体系中的多种多体量子效应，主要成果为：1）定量描绘了铁磁性RKKY作用下双量子点的相图并阐明了S=1的奇异Fermi液体态的特性；2）发现了三量子点中的Kondo云长程纠缠态并阐明了其重要的可观测特征；3）发现了由电子关联作用导致的多体隧穿效应并证明了其与Doublon动力学的密切关系；4）发现了非平衡多量子点中的铁磁相并证明了Heisenberg铁磁性起源的假说；5）从理论上实现了单空穴自旋量子位的动力学精确调控。. 本项目自主发展的非微扰计算方法解决了强关联领域的一个关键问题：量子杂质的精确求解。对于多量子点体系中多体量子效应的研究，则有助于深入理解量子多体效应和量子调控等重要问题，指导实验进行观测研究，促进量子点物理的基础研究和实际应用。