EXACT 4-SPINON DYNAMICAL CORRELATION-FUNCTION OF THE HEISENBERG-MODEL

In this paper we derive the exact expression of the four-spinon contri bution to the dynamical correlation function of the spin S = 1/2 aniso tropic (XXZ) Heisenberg model in the antiferromagnetic regime. We exte nsively study its isotropic (XXX) limit and derive perturbatively the Ising one. Our method relies on the quantum affine symmetry of the mod el, which allows for a systematic diagonalization of the Hamiltonian i n the thermodynamic limit and for an exact calculation of matrix eleme nts of local spin operators. In fact, we argue that the familiar criti cism of this method related to the complication of these matrix elemen ts is not justified. First, we give, in the form of contour integrals, an exact expression for the n-spinon contribution. After we compile r ecently found results concerning the two-spinon contribution, we speci alize the R-spinon formula to the new case n = 4. Then we give an expl icit series representation of this contribution in the isotropic limit . Finally, after we show that this representation is free of divergenc es, we discuss the Ising limit in which a simple expression is found u p to first order in the anisotropy parameter. (C) 1997 Elsevier Scienc e B.V.