Zeeman field induced corner states in the Kane-Mele-Hubbard model

We investigate how the in-plane Zeeman field and the Hubbard interaction can jointly affect the topological states in the Kane-Mele-Hubbard model. At low Zeeman field, the projector quantum Monte Carlo (PQMC) simulations demonstrate Mott transitions between the higher-order topological insulator induced by the in-plane Zeeman field and the antiferromagnetic insulator induced by the Hubbard interaction. The interacting higher-order topological state on a finite-sized honeycomb lattice is characterized by the local density of states derived from the real-space spectral function. In the higher-order topological phase, the mirror-symmetry protected corner states exist on the diamond-shaped honeycomb lattice. In terms of spatial extent of corner states induced by the in-plane Zeeman field in the Kane-Mele and Kane-Mele-Hubbard models, we show that the effect of the Hubbard interaction is to contribute some extra in-plane Zeeman field. At the mean-field level, we characterize the bulk topology by the mirror winding number and calculate the full phase diagram of the Kane-Mele-Hubbard model under the influence of the in-plane Zeeman field. The mean-field phase diagram shows that a high in-plane Zeeman field drives the system into a spin-polarized (topologically trivial) phase. In particular, the upper limit of the Zeeman field that can induce corner states in the Kane-Mele model is found to be ${h}_c=1.0$. In the parameter region of PQMC simulations, the mean-field solutions qualitatively agree with the PQMC results.