PERTURBATION EXPANSION OF THE GROUND-STATE ENERGY FOR THE ONE-DIMENSIONAL CYCLIC HUBBARD SYSTEM IN THE HUCKEL LIMIT

摘要

The perturbation expansion coefficients for the ground-state energy of the half-filled one-dimensional Hubbard model with N = 4 nu + 2, (nu = 1, 2,...) sites and satisfying cyclic boundary conditions were calculated in the Huckel limit (U/beta-->O), where beta designates the one-electron hopping or resonance integral, and U, the two-electron on-site Coulomb integral. This was achieved by solving-order by order-the Lieb-Wu equations, a system of transcendental equations that determines the set of quasi-momenta {k(i)} and spin variables {tau(alpha)} for this model. The exact values for these quantities were found for the N = 6 member ring up to the 20th order in terms of the coupling constant B = U/2 beta, as well as numerically for 10 less than or equal to N less than or equal to 50, and the N = 6 Lieb-Wu system was reduced to a system of sextic algebraic-equations. These results are compared with those of the infinite system derived analytically by Misurkin and Ovchinnikov [Teor. Mat. Fiz. 11, 127 (1972)]. It is further shown how the results of this article can be used for the interpolation by the root of a polynomial It is demonstrated that a polynomial of relatively small degree provides a very good approximation for the energy in the intermediate coupling region. (C) 1995 John Wiley & Sons, Inc. [References: 21]