Title: Phase diagram for the extended Hubbard model on a square lattice

Abstract: The Extended Hubbard model describes electron-electron interactions and is commonly used to understand various phenomena in strongly correlated systems. In this paper, we focus on investigating the phase diagram of this model, which considers a nearest neighbor interaction, $V$, in addition to the on-site term $U$. To perform our study, we utilize the determinant quantum Monte Carlo method simulations, where the average sign of the determinant is used to extract information about the quantum critical points. When both $U$ and $V$ are positive, the on-site term favors antiferromagnetism (AFM), while the extended interaction favors the formation of a charge density wave (CDW). In cases where at least one of the interactions is negative, superconductivity competes with the above-mentioned phases, and the system displays phase separation for intense attractive extended interaction. Our findings indicate that only $s$-wave and $d$-wave pairing symmetries exist in such scenarios.