t-U-W model of a d(x2-y2) superconductor in the proximity of an antiferromagnetic Mott insulator: Diagrammatic studies versus quantum Monte Carlo simulations

We examine the competition and relationship between an antiferromagnetic (A F) Mott insulating state and a d(x2-y2) superconducting (SC) State in two d imensions using semianalytical, i.e., diagrammatic calculations of the t-U- W model. The AF Mott insulator is described by the ground state of the half filled Hubbard model on a square lattice with on-site Coulomb repulsion U and nearest-neighbor single-particle hopping t. To this model, an extra ter m W is added, which depends upon the square of the single-particle nearest- neighbor hopping. Staying at half band filling and a constant value of U! i t was previously shown with quantum Monte Carlo (QMC) simulations that one can generate a quantum transition as a function of the coupling strength W between an AF Mott insulating state and a d(x2-y2) SC state. Here we comple ment these earlier QMC simulations with physically more transparent diagram matic calculations. We start with a standard Hartree-Fock (HF) calculation to capture the "high-energy" physics of the t-U-W model. Then, we derive an d solve the Bethe-Salpeter equation, i.e., we account for fluctuation effec ts within the time-dependent HF or generalized random-phase approximation s cheme. Spin and charge susceptibility as well as the effective interaction vertex are calculated and systematically compared with QMC data. Finally, t he corresponding BCS gap equation obtained for this effective interaction i s solved.