SPIN-WAVE VELOCITY AND SPECIFIC-HEAT OF THE HUBBARD-MODEL AT HALF FILLING WITH A PATH-INTEGRAL APPROACH

A path-integral formulation of the two-dimensional Hubbard model is used in which scattering of electrons across the magnetic Brillouin zone by spin fluctuations (umklapp processes) is included. With this formulation, we have calculated the spin-wave velocity c(s) and the specific heat C(v) for the half-filled-band case. For the quadratic form of the Hubbard model due to Schrieffer, we obtain c(s) = 1. 5c0 in the large-U limit (U is the intrasite Coulomb repulsion, c0 = square-root 2J is the spin-wave velocity in linear-spin-wave theory, J = 4t2/U is the superexchange interaction, and t is the hopping integral for nearest neighbors). Our result is in good agreement with various numerical calculations based on the Heisenberg model, e.g., c(s) = 1.22c0 by Liu and Manousakis [Phys. Rev. B 40, 11437 (1989)], with use of the variational Monte Carlo technique. Our present calculation differs from previous path-integral calculations, which lead to c(s) approximately t in the large-U limit. A general free-energy formula, which includes all kinds of fluctuation, is obtained. At low temperature, the specific heat in the large-U limit is given by C(v) congruent-to 0.51(T/J)2. The present calculation can also be applied to the Hubbard model written in other quadratic forms, in one of which the saddle-point approximation leads to the Hartree-Fock solution and c(s) = c0 and C(v) = 1.15(T/J)2 in the large-U limit.