  We examine the competition and relationship between an antiferromagnetic (AF)
Mott insulating state and a d_{x^2-y^2} superconducting (SC) state in two
dimensions using semi-analytical, 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 term 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, it 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_{x^2-y^2} SC state. Here we
complement these earlier QMC simulations with physically more transparent
diagrammatic 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 and solve the Bethe-Salpeter equation, i. e. we account for fluctuation
effects within the time-dependent HF or generalized RPA scheme. Spin- and
charge-susceptibility as well as the effective interaction vertex are
calculated and systematically compared with QMC data. Finally, the
corresponding BCS gap equation obtained for this effective interaction is
solved.
