Exactly solvable D-N-type quantum spin models with long-range interaction

Abstract

We derive the spectra of the D-N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D-N type. In particular, we show that this partition function cannot be obtained as a limiting case of its BCN counterpart. With the help of the partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.