论文标题
绿色的功能方法与高阶拓扑绝缘子相互作用
Green's Function Approach to Interacting Higher-order Topological Insulators
论文作者
论文摘要
Bloch波函数在非相互作用系统中拓扑阶段的诊断中起着至关重要的作用。但是，Bloch波不再适用于有限的库仑相互作用，需要替代方法来识别拓扑指数。在本文中，我们着重于受$ C_4T $对称性保护的三维高阶拓扑绝缘子，并表明可以通过零频率以零频率的函数来计算拓扑指数。如果还有额外的$ S_4 $ rotoinversion对称性，则可以在高对称矩阵上的特征值$ s_4 $确定拓扑索引$ p_3 $，类似于fu-kane Parity Criterion。我们使用具有相互作用的高阶拓扑绝缘子中多体精确对角线化来验证这种方法。我们还讨论了以$ C_4T $ preservining磁性顺序的四方晶格结构中这个高阶拓扑阶段的实现。最后，我们讨论了铰链状态出现所需的边界条件，并表明即使边界平滑且没有锋利的铰链，这些铰链状态也存在。
The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in non-interacting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-order topological insulators protected by $C_4T$ symmetry and show that the topological index can be computed through eigenstates of inverse Green's function at zero frequency. If there is an additional $S_4$ rotoinversion symmetry, the topological index $P_3$ can be determined by eigenvalues of $S_4$ at high symmetry momenta, similar to the Fu-Kane parity criterion. We verify this method using many-body exact diagonalization in higher-order topological insulators with interaction. We also discuss the realization of this higher-order topological phase in tetragonal lattice structure with $C_4T$-preserving magnetic order. Finally, we discuss the boundary conditions necessary for the hinge states to emerge and show that these hinge states exist even when the boundary is smooth and without a sharp hinge.
