Analytic calculation of second-order perturbation energy for the one-dimensional Hubbard model in the Hueckel limit

摘要

The study of the Hueckel limit for the one-dimensional Hubbard model is very complicated. It is necessary to prepare the Lieb-Wu system of equations for expansion and then to initialize the variables which appear in the system, which is not straightforward. However, it is remarkable that, for the second-order contribution to the energy in this limit, it is possible to obtain, after complicated manipulations, quite transparent expressions. The analytical solution is obtained order by order for the variables to β~(-2) which appear in the Lieb-Wu solution and the β~(-1) coefficient in the energy is calculated using these expansions. The energy can be calculated numerically using these analytic results for the variables for increasing values of N.