Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions

Abstract

Motivated by exploring the effect of interactions on Chern insulators, and by recent experiments realizing topological bands for ultracold atoms in synthetic gauge fields, we study the honeycomb lattice Haldane-Hubbard model of spin-$1/2$ fermions. Using an unrestricted mean field approach, we map out the instability of the topological band insulator towards magnetically ordered insulators which emerge with increasing Hubbard repulsion. In addition to the topological Néel phase, we recover various chiral noncoplanar magnetic orders previously identified within a strong coupling approach. We compute the band structure of these ordered phases, showing that the triple-$Q$ tetrahedral phase harbors topological Chern bands with large Chern numbers.

7 pages, 6 figures, PRB version

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• Two-component quantum Hall effects in topological flat bands
• Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model
• An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
• Spontaneous symmetry breaking of an interacting Chern insulator on a topological square lattice
• Lattice symmetry and emergence of antiferromagnetic quantum Hall states
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Interaction-induced phase transitions of type-II Weyl semimetals
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Emergence of asymmetric fermionic order in interacting birefringent fermions
• Repulsive Fermi gases in a two-dimensional lattice with non-Abelian gauge fields
• Topological order in the Haldane model with spin-spin on-site interactions
• The odd-parity altermagnetism: A spin group study
• Odd-parity altermagnetism through sublattice currents: From Haldane-Hubbard model to general bipartite lattices
• Topological hard-core bosons on the honeycomb lattice