COMPLETE ANALYSIS OF 2 SPIN CORRELATIONS OF VALENCE BOND SOLID CHAINS FOR ALL INTEGER SPINS

For the valence bond solid (VBS) chain ground state introduced by Affleck et al. we evaluate exactly all 2S two-point correlation functions for all integer spins S with a simple transfer matrix method. These correlations are expectation values of 2S different two-site irreducible tensor operators also presented in this article. Each of the first S correlations exhibits its own purely exponential decay whereas the others vanish. It turns out that in the large S limit there are both very large and very short ranged correlations. We use the correlation functions to calculate the probabilities that two spins at distance r add up to total spin-sigma and also derive a formula for the probability that two spins at distance r enclose an angle theta. This provides a complete and perspecuate description of the VBS state for arbitrary integer spin S.