Superconducting and magnetic fluctuations of the two-dimensional Hubbard model

Abstract

A new approximation scheme, the effective interaction approach (EIA), is introduced. It treats spin, charge, and pair fluctuations on an equal footing in Hubbard-type models. Apart from satisfying the Pauli principle, it also fulfills a number of other constraints that are missed in perturbation theory, in a tractable way. The EIA can be seen as a natural extension of the two-particle self-consistent approach (TPSC) of Vilk et al., and is able to deal with competing instabilities, including in principle non-local pairing effects. The resulting equations are solved numerically to yield a phase diagram displaying the competition between magnetism and d-wave superconductivity. Unlike simple-minded RPA calculations, our self-consistent scheme shows that superconductivity is depressed by the interference between the channels down to temperatures J/10, in contrast to real systems. The charge structure factor is also found to be a non-monotonic function of density, in agreement with QMC simulations and TPSC.