Quantum cluster approach to the spinful Haldane-Hubbard model

TL;DR

This paper investigates the phase diagram of the spinful Haldane-Hubbard model at half filling using advanced quantum cluster methods, revealing transitions between topological and magnetic insulating phases across interaction strengths.

Contribution

It applies cluster perturbation theory, VCA, and CDMFT to explore intermediate interaction regimes, improving upon mean-field approaches by capturing local quantum fluctuations.

Findings

Identifies a correlated topological Chern insulator at weak interactions.

Finds a topologically trivial Néel antiferromagnetic insulator at strong interactions.

Suggests possible stabilization of topologically nontrivial phases at intermediate interactions.

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 N\'eel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial N\'eel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.