强关联体系中的玻色对称保护拓扑态与分形子拓扑态的有效理论

“玻色对称保护拓扑态”和“分形子拓扑态”是强关联拓扑自旋系统中的两大前沿课题，是强关联拓扑物态网络中的重要组成部分。以 Haldane 自旋链为代表的玻色对称保护拓扑态是一类“几乎无特征”的自旋液体：其体内没有拓扑激发，但有对称保护的非平凡量子反常边界态。另外，以Vijay-Haah-Fu自旋模型为代表的分形子拓扑态是一种新型拓扑序，没有定义良好的“热力学极限”。分形子拓扑态的体内拓扑激发被称为“分形子”(fracton)，无法被局域幺正算符移动位置。本项目将运用强关联中的理论和数值方法来深入研究这两种拓扑物态。项目研究内容主要有：玻色对称保护拓扑态的 Gutzwiller 投影波函数与Hubbard相互作用；空穴掺杂的玻色对称保护拓扑态的t-J模型；分形子拓扑态的严格可解模型的构造、分形子拓扑态与玻色对称保护拓扑态之间的对偶。对上述两种物态的平行研究将有助于深入理解强关联拓扑物态网络。

As key ingredients of the network of strongly-correlated topological phases of matter, bosonic symmetry-protected topological phases (BSPT) and fracton topological phases (FT) are currently frontier of strongly-correlated topological physics. Represented by Haldane spin chain, BSPTs can be regarded as "almost featureless" quantum spin liquids whose bulk doesn’t support topological excitations but the boundary supports symmetry-protected quantum anomaly. On the other hand, represented by Vijay-Haah-Fu model, FT is a brand-new topological order, whose thermodynamical limit is ill-defined. The bulk topological excitation of FT is called "fracton" which is unable to be moved by any local unitary operators. In this proposal, theoretical and numerical methods of strongly-correlated physics will be applied to study BSPT and FT in three aspects. First, the Gutzwiller projected wavefunction and Hubbard interaction term. Second, hope-doped BSPT and its t-J model. Third, construction of exactly solvable models of FT states, and the duality between FT and BSPT. The parallel study of BSPT and FT will be beneficial to deepen our understandings on the network of strongly-correlated topological phases of matter.