Finite-size scaling in one-dimensional quantum liquid with long-range interaction

Finite-size scaling analysis is performed for one-dimensional Bose and Fermi systems with long-range interaction g/${\mathit{r}}^2$, based on the exact solution of Sutherland. The low-energy behavior of this model is shown to be described by the c=1 conformal field theory. Exact formulas for various correlation exponents are obtained. At a special point g=4, the model belongs to the same universality class as the Haldane-Shastry model, the effective theory of which is the level-1 SU(2) Kac-Moody theory.