Ground-state energy on the one- and two-dimensional Hubbard model calculated by the method of Singwi, Tosi, Land and Sjoelander

By using the classic approximation method of Singwi, Tosi, Land and Sjoelander (STLS), we calculate the ground-state energy of the one- and two-dimensional Hubbard model in the half-filled antiferromagnetic state. In the one-dimensional case, by comparison with the exact result of Lieb and Wu, we find that the STLS correlation energy competes in quality with the best values obtained from variational calculations based on the antiferromagnetic Gutzwiller wave function (AFGWF). In two dimensions, where the exact energy is not known, we find a similar relationship between the results of STLS and AFGWF calculations. For large values of U, in both dimensions, the STLS method runs into difficulties, due to the insufficient treatment of transverse spin fluctuations. (author). 18 refs, 1 fig., 2 tabs