1/4 is the new 1/2 when topology is intertwined with Mottness

Abstract

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. Here we show using determinantal quantum Monte Carlo 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 $T=0$. 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.

Figure 4e,f added as well as a reference

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• Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Topological Green's function zeros in an exactly solved model and beyond
• Real-space analysis of Hatsugai-Kohmoto interaction
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
• A Simple Solvable Model for Heavy Fermion Superconductivity from the Two-Fluid Normal State
• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
• Fate of gapless edge states in two-dimensional topological insulators with Hatsugai-Kohmoto interaction
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Incipient quantum spin Hall insulator under strong correlations
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
• Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases
• Topological phase transition driven by Hatsugai-Kohmoto interaction on the Kagome lattice
• Exact analysis of the interplay of charge order and unconventional pairings in the 2D Hatsugai-Kohmoto model
• Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry