Superconducting Phases of the Square-Lattice Extended Hubbard Model

We study the square-lattice extended Hubbard model with on-site $U$ and nearest-neighbor $V$ interactions by exact diagonalization. We show that non-equilibrium quench dynamics can help determine the equilibrium phase transition boundaries, which agree with the calculations of fidelity metric, dynamical structure factor, and correlation function. At half filling, the phase diagrams in the strong-coupling regime include spin density wave and $d_{x^2-y^2}$-wave superconductivity at large positive $U$, charge density wave (extended $s^*$-wave superconductivity) at large positive (negative) $V$, and $s$-wave superconductivity at large negative $U$ with vanishing $V$. The energies of different particle sectors also help determine the phase separation region. With carrier doping, charge fluctuation result in strong competition between different orders, making it more difficult to identify the leading instability on finite-size cluster. Nevertheless, the more exotic $p$-wave superconducting pairing is found to be enhanced when the system is heavily overdoped by $37.5\%-50\%$ holes, especially in interaction parameter range relevant to the cuprate superconductors.