DYNAMICAL T=0 CORRELATIONS OF THE S=1/2 ONE-DIMENSIONAL HEISENBERG-ANTIFERROMAGNET WITH 1/R(2) EXCHANGE IN A MAGNETIC-FIELD

We present a selection rule for matrix elements of local spin operators in the S = 1/2 Haldane-Shastry model. Based on this rule we extend a recent exact calculation by Haldane and Zirnbauer of the ground-state dynamical spin correlation function S(ab)(n,t) = [0\S(a)(n,t)S(b)(0,0)\0] and its Fourier transform S(ab)(Q,E) of this model to a finite magnetic field. In zero field, only two-spinon excitations contribute to the spectral function; in the (positively) partially spin-polarized case, there are two types of elementary excitations: spinons (DELTAS(z) = +/- 1/2) and magnons (DELTAS(z) = -1). The magnons are divided into left- or right-moving branches. The only classes of excited states contributing to the spectral functions are (I) two spinons, (II) two spinons + one magnon, (IIIa) two spinons + two magnons (moving in opposite directions), and (IIIb) one magnon. The contributions to the various correlations are S-+: (I); S(zz): (I)+(II); S+-: (I)+(II)+(III). In the zero-field limit there are no magnons, while in the fully polarized case, there are no spinons. We discuss the relation of the spectral functions to correlations of the Calogero-Sutherland model at coupling lambda = 2.