Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

Abstract

We derive the exact expression of the four-spinon contribution S4 to the dynamical correlation function S of the spin 1 2 isotropic (XXX) Heisenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S2. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S4 that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S4 corrects only by a small amount the contribution from S2.