t-U-W model of a dx2−y2 superconductor in the proximity of an antiferromagnetic Mott insulator: Diagrammatic studies versus quantum Monte Carlo simulations

Abstract

We examine the competition and relationship between an antiferromagnetic (AF) Mott insulating state and a dx2−y2 superconducting (SC) state in two dimensions 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 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 dx2−y2SC 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 random-phase approximation 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.

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