The exactly solvable spin Sutherland model of B_N type and its related spin chain

Abstract

We compute the spectrum of the su(m) spin Sutherland model of B_N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BC_N counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of B_N type is equivalent to that of a suitable vertex model, as is the case for its A_{N-1} counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.

Typeset in LaTeX (24 pages, 4 figures). arXiv admin note: text overlap with arXiv:0909.2968

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• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators