Jc. Talstra et Fdm. Haldane, DYNAMICAL T=0 CORRELATIONS OF THE S=1 2 ONE-DIMENSIONAL HEISENBERG-ANTIFERROMAGNET WITH 1/R(2) EXCHANGE IN A MAGNETIC-FIELD/, Physical review. B, Condensed matter, 50(10), 1994, pp. 6889-6899
We present a selection rule for matrix elements of local spin operator
s 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 ma
gnetic field. In zero field, only two-spinon excitations contribute to
the spectral function; in the (positively) partially spin-polarized c
ase, 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 co
ntributing to the spectral functions are (I) two spinons, (II) two spi
nons + one magnon, (IIIa) two spinons + two magnons (moving in opposit
e directions), and (IIIb) one magnon. The contributions to the various
correlations are S-+: (I); S(zz): (I)+(II); S+-: (I)+(II)+(III). In t
he zero-field limit there are no magnons, while in the fully polarized
case, there are no spinons. We discuss the relation of the spectral f
unctions to correlations of the Calogero-Sutherland model at coupling
lambda = 2.