Correlation effects in quadrupole insulators: A quantum Monte Carlo study

The quadrupole insulator, a higher-order topological insulator, with on-site Hubbard interaction is numerically studied by large-scale projector quantum Monte Carlo simulations. The Green's function formalism is successfully used to characterize topological properties in interacting quadrupole insulators. We find that the topological quadrupole insulator is stable against weak interactions and turns into a trivial antiferromagnetic insulator by a continuous topological phase transition (TPT) for strong interactions. The critical exponents related to the TPT are estimated to be $\ensuremath{\nu}=0.67(4)$, $\ensuremath{\beta}=0.40(2)$, which are consistent with the three-dimensional Heisenberg universality class.