二维拓扑强关联体系中的奇异量子态与拓扑量子相变

This project plans to study strongly correlated fermions and bosons in time-reversal-symmetry-breaking topological bands (with topological properties characterized by Chern numbers), by the exact numerical methods based upon exact diagonalizations. We aim to find new exotic quantum many-body topological phases, investigate the strong correlation effects on single-particle topological phases, and also study possible topological quantum phase transitions induced by interactions. This project is going to broaden the current rearch area by studing correlation effects in some representatvie and generic topological band models on one respect, and also try to deepen the current understanding by finding new topological quantum phases on the other aspect. We aim to open one or two new research subfields, e.g. try to find the convincing numerical evidence of some possile lattice-symmetry-breaking topological phases, and try to and find the convincing numerical evidence of topological non-Fermi liquids.

本项目计划使用基于严格对角化等技术的精确数值方法，研究时间反演对称破缺的拓扑能带（其拓扑性质由Chern数表征）上强关联相互作用的费米子与玻色子体系，致力于发现新奇的量子多体拓扑相，探讨强关联效应对单粒子拓扑相的影响，也探索相互作用导致的可能的拓扑量子相变。该项目研究一方面致力于拓宽目前拓扑能带强关联效应的研究范围，另一方面致力于深入发现新的可能的拓扑量子态。我们争取开辟一到两个新的前沿子领域，比如争取发现晶格对称破缺型拓扑相的数值证据,争取发现拓扑型非费米液体相的数值证据。

在该研究项目执行中，我们取得如下代表性研究成果：发现分数陈绝缘体的手征Luttinger液体边缘激发；成功构建分数陈绝缘体的量子多体波函数；二维拓扑超导体中的多种拓扑量子相变；二维拓扑超导体拓扑性质的组合拓扑数表征；奇异几何结构上陈绝缘体的分数化电荷与多重边缘激发谱。此外，我们在奇异几何结构上研究相互作用的分数陈绝缘体中也得到多重边缘激发谱，在碟形几何结构陈绝缘体态中探究拓扑量子相变等。该项目研究成果一方面给出了构造拓扑量子态多体波函数的新数值方法，拓展了（分数）陈绝缘体态的拓扑性质与分数化现象的了解；另一方面给出二维拓扑超导态之间一系列拓扑量子相变的丰富相图以及组合表征方案。