Fermion description of a Heisenberg spin system

Abstract

To avoid the complications associated with the commutation relations for spin operators inherent in the more usual approaches to a theory of the Heisenberg model, Pratt and Puff introduced an electronic model in which a strong repulsion between electrons caused the electron system to simulate the Heisenberg model, but met with difficulties in treating the strong repulsion as a perturbation. In this paper it is shown how the theory may be made sound by a more rigorous treatment of the strong repulsion. The results obtained in the lowest order are shown to be equivalent to Weiss molecular field theory for the single-particle Green function and the random phase approximation to spin-wave theory for the two-particle Green function. The S² sum rule is shown to be satisfied in both the high- and low-temperature limits, but not at intermediate temperatures and a method of renormalization based on this sum rule is suggested.