Quantum Magnetism in Wannier-Obstructed Mott Insulators

We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier-obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree–Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier-obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest-neighbor orbital overlap g, this model exhibits stable ferromagnetism up to a finite bandwidth W∼Ug, where U is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier-obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier-obstructed bands.