Application of the Hard-Core Boson Formalism to the Heisenberg Ferromagnet

The rigorous method developed in a previous paper for the calculation of the time-dependent properties of localized spin systems is applied to the case of the arbitrary-spin isotropic Heisenberg model of ferromagnetism. A low-density approximation is used to calculate the spin Green's function G₁(1; 1^')=-i〈TS^-(1)S⁺(1^')〉 within the framework of this formalism. For the special case of S=1/2, it is explicitly demonstrated that the nonphysical states produce errors that may not be exponentally small, and that in the hard-core limit these terms disappear. The results of this work prove that for arbitrary S the "truncated" version of the Holstein-Primakoff transformation written in normal product form will produce the correct low-temperature results to all orders in 1/2S. The form of the space-time transform G₁(p; z) of G₁(1; 1^') that we obtain is different from that suggested by previous work, since it does not contain any function of p or z in the numerator. In fact, if our result is expanded at temperatures low enough, the first term in the expansion is exactly the result obtained for G₁(p; z) by Silberglitt and Harris from the Dyson transformation by neglecting the effects of the nonphysical states.