ANALYTIC CALCULATION OF 2ND-ORDER PERTURBATION ENERGY FOR THE ONE-DIMENSIONAL HUBBARD-MODEL IN THE HUCKEL LIMIT

The study of the Huckel limit for the one-dimensional Hubbard model is very complicated. It is necessary to prepare the Lieb-Wu system of eq uations for expansion and then to initialize the variables which appea r in the system, which is not straightforward. However, it is remarkab le that, for the second-order contribution to the energy in this limit , it is possible to obtain, after complicated manipulations, quite tra nsparent expressions. The analytical solution is obtained order by ord er for the variables to beta(-2) which appear in the Lieb-Wu solution and the beta(-1) coefficient in the energy is calculated using these e xpansions. The energy can be calculated numerically using these analyt ic results for the variables for increasing values of N.