Dynamical T=0 correlations of the S=1/2 one-dimensional Heisenberg antiferromagnet with 1/r2 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 Sab(n,t)=0Sa(n,t)Sb(0,0)0 and its Fourier transform Sab(Q,E) of this model to a finite magnetic field. In zero field, only two-spinon excitations contribute to the spec tral function; in the (positively) partially spin-polarized case, there are two types of elementary excitations: spinons (ΔSz=±1/2) and magnons (ΔSz=-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); Szz: (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 λ=2.