  The quadrupole insulator, a high-order topological insulator, with on-site
Hubbard interaction is numerically studied by large-scale projector quantum
Monte Carlo (PQMC) simulations. The Green's function formalism is successfully
used to characterize topological properties in interacting quadrupole
insulators for the first time. We find that the topological quadrupole
insulator is stable against weak interactions and turns into a trivial
antiferromagnetic (AFM) insulator by a continuous topological phase transition
(TPT) for strong interactions. The critical exponents related to the TPT are
estimated to be $\nu=0.67(4)$, $\beta=0.40(2)$, which are distinct from those
of the known AFM transitions and suggest a new universality class.
