To assess prior mean-field claims that the interacting Kane-Mele model hosts a novel $z\text{−}\mathrm{antiferromagnetic}$ (AFM) Chern insulating phase for a wide range of sublattice potentials, we analyze the Kane-Mele-Hubbard model in the presence of a sublattice potential using nonperturbative determinant quantum Monte Carlo simulations. We find instead that the true low-temperature state is a quantum spin Hall insulator for intermediate values of the sublattice potential ${\lambda }_v$ and large on-site repulsion. Two kinds of magnetic fluctuations are found to compete: $z\text{−}$ and $xy\text{−}\mathrm{AFM}$. The latter dominates at low temperature leading to a stabilization of the quantum spin Hall state as opposed to $\mathrm{a}z\text{−}\mathrm{AFM}$ Chern insulator. Our work is consistent with the robust quantum spin Hall effects which are consistently observed at even-integer fillings over a wide range of parameters in twisted bilayer ${\mathrm{MoTe}}_2$ and ${\mathrm{WSe}}_2$ as well as AB-stacked ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$.

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• Kane-Mele model
• Quantum spin Hall effect
• Topological insulators
• Transition metal dichalcogenides
• Hubbard model
• Quantum Monte Carlo