Correlation functions and critical exponents in the one-dimensional anisotropict-Jmodel

The momentum distribution and the spin-correlation functions are studied for the one-dimensional t-J model, in which the exchange interaction J is anisotropic. The discussion is focused on the nontrivial limit that J is much smaller than t. In this limit the exact ground-state wave function is a product of the spinless-fermion Slater determinant and the spin-wave function of the s=1/2 anisotropic Heisenberg antiferromagnet. With this wave function, correlation functions are calculated explicitly for finite but large systems and the nature of their singularities is studied. It is found that for the XY-like anisotropy the critical behavior of correlation functions can be described by the Tomonaga-Luttinger model, while for the Ising-like anisotropy the model seems to belong to the universality class of the Luther-Emery model of the one-dimensional electron gas.