Quantum Anomalous Hall Effect in Flat Bands with Paramagnetism

Quantum anomalous Hall effect has been widely explored in both ferromagnetic and antiferromagnetic systems. Here, we propose an interaction-driven paramagnetic quantum anomalous Hall effect emerging in the Fermion-Hubbard model on a dice lattice with weak spin-orbit coupling. Based on exact diagonalization calculations, the time-reversal symmetry breaking in the ground state is evidenced by nonuniform loop currents between nearest-neighbor sites. The many-body ground state possesses a Chern number of $\mathcal{C}=2$ or $6$, and strong correlation effects in the half-filled flat bands lead to a well-defined first excitation gap and a clear insulating gap, ensuring the robustness against thermal fluctuations and external perturbations. The interplay between spin-orbit coupling and Hubbard interaction allows tunability of various magnetic ground states, generating a rich phase diagram with competing ferromagnetic, antiferromagnetic, and paramagnetic orders.