Topological insulators under strong correlations

Here we explore the fundamental interplay between topology and Mottness. Using determinant quantum Monte Carlo (DQMC) simulations, we first investigate interacting quantum Hall systems across various lattice geometries, including square, honeycomb, and triangular lattices. Our results reveal ferromagnetic quantum Hall states at odd integer fillings in these systems. Expanding on this, we examine correlation effects in spinful topological bands without an external magnetic field. In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. We show using DQMC and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at zero temperature. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moire systems.