Effect of Exclusion of Double Occupancies in t-J Model: Extension of   Gutzwiller Approximation
  A new type of analytic estimation of the effect of strong correlation is developed for the two-dimensional t-J model. It is based on the Gutzwiller approximation which gives the renormalization of parameters, t and J, due to the Gutzwiller's projection operator excluding the double occupancies. The finite-range correlations are taken into account compared with the conventional Gutzwiller approximation where only the on-site expectation values are considered. It is shown that the essential point of the renormalization is its nonlinear dependence on the expectation values of Cooper pairs and antiferromagnetic moment. In particular the renormalization factor of J becomes anisotropic in the presence of antiferromagnetic moment, i.e., that for the z-component is enhanced compared with that for the xy-component. The physical origin of this enhancement is identified as the surrounding antiferromagnetic correlations of a bond. The self-consistency equations for the uniform variational wave functions are derived and solved numerically. Our result gives a reasonable estimate of antiferromagnetic order parameters near half filling, in contrast to the conventional slave-boson mean-field theory and the original Gutzwiller approximation. It is also found that, at half filling, the renormalization of J represents some of the quantum fluctuations of the Heisenberg spin system in a different manner from the spin-wave theory. For finite doping, our results have some similarity to SO(5) symmetric theory. Applications to the inhomogeneous systems such as the vortex state, around nonmagnetic impurities, and stripe state are discussed. 
M. Ogata and A. Himeda