In this Letter I mainly consider a finite XXZ spin chain with periodic boun
dary conditions and an odd number of sites. This system is described by the
Hamiltonian H-xxz = - Sigma (N)(j=1){sigma (x)(j)sigma (x)(j+1)+sigma (y)(
j)sigma (y)(j+1) + Delta sigma (z)(j)sigma (z)(j+1)}. As it turns out, the
ground state energy is proportional to the number of sites E = -3N/2 for a
special value of the asymmetry parameter Delta = -1/2. The trigonometric po
lynomial Q(u), the zeros of which are parameters of the ground state Bethe
eigenvector, Is explicitly constructed. This polynomial of degree n = (N -
1)/2 satisfies the Baxter T-Q equation. Using the second independent soluti
on of this equation that corresponds to the same eigenvalue of the transfer
matrix, it is possible to find a derivative of the ground state energy w.r
.t. the asymmetry parameter. This derivative is closely connected with the
correlation function [sigma (z)(j)sigma (z)(j+1)] = -1/2 + 3/2N(2). This co
rrelation function is related to the average number of spin strings for the
ground state [N-string] = 3/4(N - 1/N). I would like to stress that all th
e above simple formulae are not applicable to the case of an even number of
sites which is usually considered.