Superconducting condensation energy computed for the 2D Hubbard model with Bi2212-type band

The 2D Hubbard model is the simplest model that possibly explains the occurrence of high-T c superconductivity (SC) in cuprates. To demonstrate this possibility with a condition of moderate on-site Coulomb energy U, we have computed the SC condensation energy E cond by means of the variational Monte Carlo method employing a slightly modified Gutzwiller trial wave function which also takes account of the Bi2212-type band, i.e., t' ∼ -0.34 and t'' ∼ 0.23 (t, t' and t'' are defined in the main text; energy unit is t). The competing SDW E cond strongly depended on the employed lattice size L x L but approached the bulk-limit value when L ≥ 16. With proper assumption on the value of t'', the t' region where the SDW E cond are larger than the SC E cond shrank to -0.16 ≤ t' ≤ -0.08. In -0.40 < t' < -0.16 the SC E cond was found predominant. Concerning the lattice-size dependence the SC E cond in the neighborhood of the Bi2212-type set was found to tend to increase with increasing L when L ≥ 16, taking about 1/3 or 1 times the experimental SC E cond of YBCO. This was computed using periodic boundary conditions (bc's) for the two directions. The average of two results for periodic and antiperiodic bc's imposed to both x- and y-directions for t' = -0.31 and t'' = 0.21 proved to make the L-dependence so mild that the extrapolation to the finite bulk limit looks plausible. Together with the previous positive result with t' ∼ -0.05 and t'' = 0, this result clearly supports the applicability of the 2D Hubbard model to the SC in the whole group of cuprates. Incidentally, more elaborate Gutzwiller-Jastrow-type trial functions were also examined but found to bring in only minor differences