Half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations

The extended Hubbard model describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-${T}_c$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, $s$- and $d$-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, ${T}_c(U,V)$, featuring critical temperatures for the charge-density wave and $s$-wave superconducting phases.