Many-body multipole indices revealed by the real-space dynamical mean-field theory

Abstract: The multipole moments are fundamental properties of insulators, and have attracted lots of attention with emerging of the higher-order topological insulators. A couple of ways, including generalization of the formula for the polarization and the Wilson loop, have been proposed to calculate it in real materials. However, a practical method to explore it in correlated insulators is still lacking. Here, we proposed a systematic way, which combines the general Green's function formula for multiopoles with the real-space dynamical mean-field theory, to calculate the multipole moments in correlated materials. Our demonstrating calculations are consistent with symmetry analysis, and the calculations of the spectral functions further confirm our results. This method opens the new avenue to study the topological phase transitions in correlated multipole insulators and other crucial physical quantities closely related to multipole moments.