Competing chiral orders in the topological Haldane-Hubbard model of spin-12fermions and bosons

Abstract

Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-1/2 fermions. We find that slave rotor mean field theory yields gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-1/2 bosons. Finally, we point out possible experimental implications of our results for cold atom experiments.

Quantum cluster approach to the spinful Haldane-Hubbard model

“…Henceforth all energies will be measured in units of t, and we set t = 1. Previous mean-field studies [9][10][11][12][13][14][15][16][17]19 all agree on the fact that for φ = 0, π, the CI is stable against the Hubbard interaction for U less than some critical U c (φ), where the detailed form of U c (φ) depends on the approach being used. One expects the CI to be perturbatively stable against interactions because it is a gapped state.…”

“…However, different approaches lead to different conclusions regarding what phases occur for U > U c (φ), and in what order. Most conventional mean-field studies predict the occurrence of magnetically ordered phases at large enough U, [14][15][16][17]19 while slave-particle studies predict additional nonmagnetic, topologically ordered phases at intermediate U, such as the chiral spin liquid (CSL) 9,15,[59][60][61][62] and the correlated Chern insulator (CI*). 13,17 The possibility of a CSL ground state in models of CIs augmented by an on-site Hubbard repulsion can also be inferred from Gutzwiller-projection studies of such models 63 and ED studies of effective spin Hamiltonians in the large-U limit.…”

“…1, in this paper we aim to determine the ground-state phase diagram of the half-filled spinful Haldane-Hubbard (HH) model. [9][10][11][12][13][14][15][16][17][18][19] This model can be seen as a hybrid of the standard Haldane and Hubbard models, in which spin-1/2 fermions hop on a twodimensional (2D) honeycomb lattice according to Haldane's original tight-binding model, but also repel each other when on the same site with energy cost U (Fig. 1).…”

“…The first is the large-U limit, in which the HH model at half filling is mapped to an effective SU(2)-invariant spin model involving only the spin degree of freedom of the original fermions. The resulting spin model has been studied using classical variational approaches 15 as well as exact diagonalization (ED) on small clusters. 18 Although the large-U limit is expected to give a good description of the physics deep in the Mott insulating phase where charge degrees of freedom are frozen, it cannot describe the Mott/symmetry-breaking transitions out of the weakly interacting Chern insulating phase.…”

First-order topological phase transition of the Haldane-Hubbard model

“…Similarly, in the Haldane-Hubbard model the local onsite interaction favors an AFI in the strong coupling regime, 11,12 which competes with a Chern insulator (CI) at weak coupling. To find out how the two limiting cases are connected requires a non-perturbative treatment.…”