The well-known Gutzwiller wave function is generalized by including new variational parameters to control nearest-neighbour charge-charge, charge-spin, and spin-spin correlations. The non-magnetic state of the one-dimensional, half-filled Hubbard model is studied. Within the Gutzwiller approximation, the expression for the ground state energy can be worked out analytically. The correlation between empty and doubly occupied sites is found to play the most essential role. Minimization in the large-U limit shows that the Brinkman-Rice transition has been pushed to U → ∞, and the leading term of the ground state energy density is of order −t2/ U . In contrast to results obtained with the Gutzwiller wave function, we find that the band occupation number nk is monotonically decreasing both above and below kF. The dominant k–dependence is given by ~(t/U) cos k, in agreement with t/U–expansion results. nk has also a weak step-function component, with the discontinuity at kF vanishing as (t/U)2 in the limit U/t ≫ 1.
Exact Jastrow-Slater wave function for the one-dimensional Luttinger model
