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

TL;DR

This paper explores how in-plane Zeeman fields and Hubbard interactions influence topological states in the Kane-Mele-Hubbard model, revealing phase transitions and corner states through simulations and mean-field analysis.

Contribution

It demonstrates the joint effects of Zeeman fields and Hubbard interactions on topological phases and corner states, providing phase diagrams and comparing simulation methods.

Findings

Mott transitions between topological and antiferromagnetic insulators

Existence of mirror-inversion symmetry protected corner states

Critical Zeeman field for inducing corner states is approximately 1.0

Abstract

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-inversion symmetry protected corner states exist on the diamond-shaped honeycomb lattice. By comparing the spatial distribution of corner states between 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 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 $h_c = 1.0(3)$. In the parameter region of PQMC simulations, the mean-field solutions are in fair agreement with the PQMC results.