Quantum Magnetism in Wannier-Obstructed Mott Insulators

TL;DR

This paper develops a systematic method to derive effective spin models for Wannier obstructed Mott insulators, revealing new exchange interactions and explaining robust ferromagnetism observed experimentally.

Contribution

It introduces a diagrammatic approach to derive spin models from electron Hamiltonians in Wannier obstructed bands, accounting for nonorthogonality effects.

Findings

Stable ferromagnetism persists up to a finite bandwidth proportional to orbital overlap.

The approach explains experimentally observed ferromagnetism in Wannier obstructed bands.

Potential for studying frustrated quantum magnetism near ferromagnetic-antiferromagnetic crossover.

Abstract

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 $W\sim U g$, 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.