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

Multipole moments, fundamental characteristics of insulating materials, have garnered significant interest with the recent emergence of higher-order topological insulators. However, a practical method to explore them in correlated insulators is still lacking. Here, we introduce a systematic approach, which combines the general Green’s function formula for multipoles with real-space dynamical mean-field theory, to calculate multipole moments in correlated materials. Our demonstration calculations for the correlated two-dimensional Benalcazar–Bernevig–Hughes model are consistent with symmetry analysis. This method opens a new avenue to study topological phase transitions in correlated multipole insulators and other crucial physical quantities closely related to multipole moments.