Quantum cluster approach to the spinful Haldane-Hubbard model

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.Comment: 11 pages, 12 figures. Published versio

Doping phase diagram of a Hubbard model for twisted bilayer cuprates

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $\theta=53.13^{\circ}$ using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference $\phi$ between the $d$-wave order parameters of two layers is $\pi$ in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference $\phi$ changes continuously from 0 to $\pi$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.Comment: 8 pages, 7 figure