SU(N) generalization of the Gutzwiller-Jastrow wave function and its critical properties in one dimension

The SU(N)-generalized Gutzwiller-Jastrow wave function, which includes the effects of smooth-correlation holes, is discussed in one dimension. The long-distance critical properties are analyzed using conformal field theory, and the exact critical exponents of the correlation functions are obtained analytically. The universal scaling relations for SU(N) Luttinger liquids are derived. We also present an exactly solvable model for which the SU(N) Gutzwiller wave function gives the ground state.