t′- and t″-dependence of the bulk-limit superconducting condensation energy of the 2D Hubbard model

The 2D Hubbard model having the 2nd- and 3rd-neighbor transfer energies t′ and t″ is investigated by use of the variational Monte Carlo method. At the nearly optimal doping with on-site Coulomb energy U = 6 (energy unit is t) the condensation energy Econd for the d-wave superconductivity (SC) is computed for lattices of sizes from 10 × 10 to 28 × 28 with the aim to get its bulk-limit value. t″ is fixed at −t′/2. Outside and in the neighborhood of the SDW region of -0.16 ⩽ t′ ⩽ −0.08 the SC Econd dominates over the SDW Econd. At t′ = −0.05 and −0.10 we obtained a definitely finite bulk-limit SC Econd of the order of the experimental value for YBCO. At t′ = 0 Econd nearly vanishes. For t′ ⩽ -0.18, the SC Econd strongly oscillates as a function of the lattice size, when periodic boundary conditions (b.c.'s) are imposed to both axes. In the case of periodic and anti periodic b.c.'s, a finite bulk-limit value is obtained at t′ = −0.22. Econd tends to vanish with further decrease of t′. With our results the SC of LSCO is understandable with t′∼−0.10. The t′ values of Hg1201, Tl2201 and Na-CCOC seem close to −0.20 so that they locate in the boundary zone of SC indicated in the present work. Slightly larger U improves the situation by increasing Econd.