M. Takahashi et al., PERTURBATION EXPANSION OF THE GROUND-STATE ENERGY FOR THE ONE-DIMENSIONAL CYCLIC HUBBARD SYSTEM IN THE HUCKEL LIMIT, International journal of quantum chemistry, 53(5), 1995, pp. 457-466
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 calcu
lated in the Huckel limit (U/beta-->O), where beta designates the one-
electron hopping or resonance integral, and U, the two-electron on-sit
e Coulomb integral. This was achieved by solving-order by order-the Li
eb-Wu equations, a system of transcendental equations that determines
the set of quasi-momenta {k(i)} and spin variables {tau(alpha)} for th
is 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 le
ss 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 Ovch
innikov [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 sma
ll degree provides a very good approximation for the energy in the int
ermediate coupling region. (C) 1995 John Wiley & Sons, Inc.