Phase Diagram and Pairing Symmetry of the Two-Dimensional t-J Model by a   Variation Theory
  Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2). 
Hisatoshi Yokoyama and Masao Ogata