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

TL;DR

This paper derives the exact spectrum and degeneracies of the B_N type spin Sutherland model, computes the partition function of its related spin chain, and explores spectral properties and distribution in the large N limit.

Contribution

It provides the first exact spectrum and degeneracy calculations for the B_N type spin Sutherland model and its associated spin chain, including the partition function in closed form.

Findings

The spectrum of the B_N type spin chain cannot be obtained as a limit of the BC_N case.

The spectrum is equivalent to that of a vertex model.

Eigenvalue density approaches a normal distribution as N increases.

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.