Quantum cluster approach to the spinful Haldane-Hubbard model

Abstract

We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial Néel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial Néel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.

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

“…Also results of a variational cluster approximation calculation on 6-site clusters 33,40 indicate an indirect transition from CI to AFI, but via a topologically non-trivial non-magnetic insulating phase with opposite Chern number as the CI. Another recent study using 6-site DCA and CDMFT calculations 41 reports, similar to our findings, a signature of a first order transition for λ/t = 0.2.…”

Topological phase transitions and universality in the Haldane-Hubbard model

“…Therefore, studying its effects on the transport coefficients is of fundamental importance for the next generation of cold atom experiments. So far, the properties of the Haldane-Hubbard model have been investigated mostly via mean-field, variational and numerical analyses [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] .…”

Quantum cluster approach to the topological invariants in correlated Chern insulators

“…A divergence of the spectra of the topological Hamiltonian corresponds to the emergence of a zero-energy zero of the single particle Green's functions. Now it seems to lead us to a conclusion that the 'second topological transition' at U>U AF is a concrete realization in a microscopic model of the last scenario, as was similarly claimed in [45]. However, according to the generalized bulk-edge correspondence [58,59], a topological phase with a nonzero interacting bulk Chern number must assume gapless single particle states or zero-energy zeros of the single particle Green's function on open boundaries.…”

“…They give access to nontrivial many-body effects and can be unified within the variational principle based on the self energy functional approach [44]. These methods include cluster perturbation theory (CPT) [26], dynamical cluster approach (DCA) [27], cellular dynamical mean field theory (CDMFT) [28], variational cluster approach (VCA) [29], cluster dynamical impurity approximation [32], etc, and have been widely applied to detect the topological properties of interacting topological band insulators [21,22,34,35,38,45].…”

“…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. These intermediate phases were claimed to be topological because their interacting bulk Chern numbers constructed from the topological Hamiltonians within the natural-unit cell were shown to be nonzero.…”