HIGH-ORDER PERTURBATION EXPANSION FOR THE 2-DIMENSIONAL HUBBARD-MODEL USING THE GUTZWILLER WAVE-FUNCTION

A variational approach of the two-dimensional Hubbard model is presented, based on the Gutzwiller wave function, making no use of the Gutzwiller approximation. We calculated exactly the coefficients of the (g2-1)m expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m = 8 order. The m > 8 terms were deduced with an acuracy O[(n/2)18] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.