Application of Quantum Cluster Methods with a dynamical Hartree-Fock approximation to the extended Hubbard model

The single-band Hubbard model has been studied extensively as the prototype of physical models for strongly correlated systems. Adding extended interactions to this model can be useful for considering more realistic long-range Coulomb interactions, as well as lattice-induced attractive interactions. While this model is also well-studied, previous studies on this model have often used perturbative approaches, or focused on the half-filled limit. In this talk, I will discuss the results of our recent analysis of the square lattice extended Hubbard model, both for attractive and repulsive extended interactions, using a combination of Cluster Dynamical Mean Field theory (CDMFT), which treats the Hubbard interaction U non-perturbatively, and a Hartree-Fock mean-field decoupling of the intercluster extended interaction V, in both superconducting and particle-hole channels. We study the phase diagram of this model as a function of the filling, and examine its dependence on the couplings U and V. For attractive V, our analysis confirms d-wave superconductivity near half-filling, giving way to extended s-wave pairing as a function of doping, via a mixed s+id state. At half-filling, we study the competition of the antiferromagnetic state with superconductivity for attractive V, and charge-density wave order for repulsive V. Finally, we do not find any significant evidence of p-wave superconductivity in this model, within the parameter regimes considered by us.