Relativistic Calogero-Sutherland Model : Spin Generalization, Quantum Affine Symmetry and Dynamical Correlation Functions

Spin generalization of the relativistic Calogero-Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry Uq(ĝl2). The spin-less model is exactly diagonalized by means of the Macdonald symmetric polynomials. The dynamical density-density correlation function as well as one-particle Green function are evaluated exactly. We also investigate the finitesize scaling of the model and show that the low-energy behavior is described by the C = 1 Gaussian theory. The results indicate that the excitations obey the fractional exclusion statistics and exhibit the Tomonaga-Luttinger liquid behavior as well. Recently, Yangian symmetry has been extensively studied[1, 2, 3] in the relation to the Calogero-Sutherland model (CSM)[4], the Haldane-Shastry model (HSM)[5] as well as conformal field theory (CFT). Especially, it is remarkable that a new structure of CFT called spinon structure has been understood based on this symmetry[3]. This motived the author in [6] to analyze the analogous structure of the level-1 integrable highest weight modules of the quantum affine algebra Uq(ŝl2). These modules are known to have a deep connection with integrable spin chain models[7]. The level-0 action of Uq(ŝl2) in the level-1 modules plays the same role as the Yangian in CFT. Namely the level-1 modules are completely reducible with respect to the level-0 action. However, no physical models related to this level-0 symmetry have been discussed.