具有自旋轨道耦合的关联体系中新奇量子物态及元激发性质的研究

The interplay between the electron's spin-orbit coupling and correlation effect can induce rich and exotic quantum phenomena, which is one of the most active areas in modern condensed matter physics. Recently, the 4d and 5d transition-metal compounds have attracted much attention, and they become an ideal playground to study the interplay between spin-orbit coupling and correlation effect. But the low-energy effective models that describe these materials and the emergent new quantum phases are currently still under debate, and the theoretical study of topological phases in correlated systems needs further developments. In this project, we will use slave-particle mean-field methods, projective symmetry group and cluster perturbation theory to study exotic quantum phenomena in correlated systems with spin-orbit coupling. Specifically, we will study the possible exotic quantum phases and the quantum phase transitions between them, and reveal the correlation effects on topological phases; Moreover, we will also study the possible unconventional superconductivity induced by doping, analyze the properties of elementary excitations and the possible fractionalization phenomena. The aim of this project is to study the exotic quantum phenomena in correlated systems with spin-orbit coupling in theoretical perspective, which would help us to understand the experimental results in the 4d and 5d materials and would also provide theoretical foundations to the development of the new generation of low energy consumption electronic devices.

电子的自旋轨道耦合与关联效应之间的相互作用会导致丰富而新奇的量子现象，是当今凝聚态物理最活跃的研究领域之一。最近引起广泛关注的4d和5d过渡金属化合物材料，为研究自旋轨道耦合与关联效应的相互影响提供了良好平台。但描述这类材料物理性质的低能有效模型以及可能出现的新颖量子相仍存在众多争议，关联系统中拓扑相的理论研究仍需深入开展。本项目拟使用隶粒子平均场方法、投影对称群以及集团微扰理论等量子多体方法研究具有自旋轨道耦合的关联体系中的新奇量子现象。一方面，研究系统中可能存在的各种新颖量子物态及量子相变，揭示电子相互作用对拓扑相的影响；另一方面，研究掺杂可能引起的非常规超导电性，分析系统的元激发性质以及可能出现的分数化现象。本项目旨在理论研究具有自旋轨道耦合的关联体系中的新奇量子现象，不仅有助于理解4d和5d材料中的相关实验结果，也将为新一代低能耗电子器件的发展提供参考依据。

本项目利用量子多体系统的严格解析求解方法、自洽平均场计算以及变分集团近似等数值方法，重点研究了强关联拓扑量子体系的若干严格结果以及准粒子能谱演化等问题。一方面，我们研究了具有自旋轨道耦合的关联费米子模型中的eta配对现象。自旋轨道耦合系统通常被认为不具有连续对称性，除了一般的U(1)粒子数对称性。eta配对揭示了一大类自旋轨道耦合Hubbard模型中所隐藏的SU(2)赝自旋对称性。我们进一步构造了一个严格可解的相互作用狄拉克半金属模型，该模型具有严格的eta配对基态以及电荷密度波基态，这些对称破缺态相遇于一个严格可解的多临界相变线。另一方面，我们利用变分集团近似等数值方法研究了 Weyl 半金属的 Weyl 点在 Hubbard 相互作用下的演化情况。通过几个具体模型的计算，加上平均场方法的分析，我们发现，对称性破缺（例如铁磁序）会导致 Weyl 点随着相互作用的变化而移动。如果体系没有发生对称性破缺（例如具有时间反演或空间反演对称性），那么 Weyl 点对于相互作用具有鲁棒性。

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