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

Abstract

We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with onsite repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first order transition include hysteretic behavior of the double occupancy, single-particle excitation gap and nearest neighbor spin-spin correlations. This first order transition is contrasted with a continuous phase transition from the conventional band insulator to the antiferromagnetic insulator in the ionic Hubbard model on the honeycomb lattice.

Topological phases in the Haldane model with spin–spin on-site interactions

“…In this broad range, the momentum space mean-field theory compares favorably with the more costly and difficult MPS simulations, and the winding number provides an accurate characterization of the TI phase. For stronger interactions, the ground state becomes a Mott insulator, where, in accordance to earlier work, a non-trivial spin order may appear [14][15][16][17][18][19][20][21][22]. On account of our numerical results, we discuss a possible ultracold atom experiment that can directly simulate our model, based on previous experiments with TIs [6,7,10] and the measurement of topological properties [31].…”

“…We observe that the ground state remains in a paramagnetic phase until the repulsive interactions destroy the topological phase. The MPS results show, however, that the staggered magnetization begins to grow slightly before the repulsive topological phase transition converts the state in a topologically trivial one, U/t∼3, which could signal the existence of an intermediate topological phase, as reported by other authors [15,18,20,21] when the sublattice imbalanceò is nonzero. In the parameter space studied in this work, ò=0, this phase reduces to a single point in parameter space, which is absent in the meanfield calculations.…”

“…An interesting problem is the study of how this, or other TI models, are modified by the presence of interactions, either by destroying the topologically protected phase, or by replacing it with other non-trivial phases. Some work has already been done in the field of interacting TIs, the spinless Haldane model with nearest neighbor interactions [13], the Haldane-Hubbard model with spin and on-site interactions [14][15][16][17][18][19][20][21][22][23], the Kane-Mele model [24,25], pyrochlores [26], the synthetic Creutz-Hubbard model [27] or a general TI in the context of the fractional quantum Hall effect [28].…”

Quantum cluster approach to the topological invariants in correlated Chern insulators

“…We want to remark that the actual phase diagram of the Haldane Hubbard model in the moderate interacting regime has been highly debated over the past several years, namely different methods predicted quite different results [45][46][47][48][49][50][51][52][53][54][55][56][57]. In particular, even whether the intermediate phases exist has not come to an agreement, let alone their physical properties.…”

“…In this article we focus on the scheme of applying quantum cluster approaches to the determination of topological invariants in correlated Chern insulators. The prototype is the half-filled Haldane Hubbard model [46][47][48][49][50][51][52][53][54][55][56][57], which exhibits quantum anomalous Hall effect with weak Coulomb interactions and is antiferromagnetically ordered in the strong coupling limit. Previous quantum cluster methods [45] predicted a topological Neel antiferromagnet and/or a topological nonmagnetic Mott insulator in the moderate interacting regime.…”