Haldane-Shastry spin chains of BCN type

©2004 Elsevier B.V All rights reserved. This work was partially supported by the DGI under grant No. BFM2002–02646. A.E. acknowledges the financial support of the Spanish Ministry of Education and Science through an FPU scholarship. The authors would like to thank J. Retamosa for pointing out Ref. [30] to them.
We introduce four types of SU(2M + 1) spin chains which can be regarded as the BCN versions of the celebrated Haldane-Shastry chain. These chains depend on two free parameters and, unlike the original Haldane-Shastry chain, their sites need not be equally spaced. We prove that all four chains are solvable by deriving an exact expression for their partition function using Polychronakos's "freezing trick". From this expression we deduce several properties of the spectrum, and advance a number of conjectures that hold for a wide range of values of the spin M and the number of particles. In particular, we conjecture that the level density is Gaussian, and provide a heuristic derivation of general formulas for the mean and the standard deviation of the energy
DGI, Spain
Spanish Ministry of Education and Science
Depto. de Física Teórica
Fac. de Ciencias Físicas
TRUE
pub