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Phase diagram and mechanism of superconductivity in a strongly correlated electron system

We investigate the phase diagram of two-dimensional (2D) Hubbard model by employing the optimization variational Monte Carlo method. The 2D Hubbard model is the most simple electronic model for cuprate high-temperature superconductors. The phase diagram consists of three regions; they are antiferromagnetic insulator (AFI) region, superconducting (SC) region and the coexistent region of superconductivity and antiferromgantism. The phase diagram obtained by numerical calculations well agrees with the experimental phase diagram for high-temperature cuprates. We mainly focused on the effect of $t'$ on the antiferromagnetic (AF) correlation and the AFI region. The area of the AF phase increases when we include $t'$ and thus the pure $d$-wave SC phase decreases. The AFI phase near half filling decreases as $|t'|$ increases.