Quantum Magnetism in Wannier-Obstructed Mott Insulators

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 $W\sim Ug$, 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.

21 pages, 11 figures

References in corpus (23)

• Topological kagome magnets and superconductors
• Negative flat band magnetism in a spin-orbit coupled correlated kagome magnet
• The Hubbard Model
• Exponential localization of Wannier functions in insulators
• Magic in twisted transition metal dichalcogenide bilayers
• Half and quarter metals in rhombohedral trilayer graphene
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Programming Correlated Magnetic States via Gate Controlled Moiré Geometry
• Orbital Multiferroicity in Pentalayer Rhombohedral Graphene
• Coulomb Correlations and the Wigner-Mott Transition
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Extended Hubbard model: Charge Ordering and Wigner-Mott transition
• Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Doping driven metal-insulator transitions and charge orderings in the extended Hubbard model
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Kagome chiral spin liquid in transition metal dichalcogenide moiré bilayers
• SU(N) fractional quantum Hall effects in topological flat bands
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model