Ground-state correlations of one-dimensional quantum many-body systems

We study the correlations in a family of ground-state wave functions for one-dimensional quantum many-body systems. For a particular ordering of the M particles, these wave functions are given as the absolute value of the free-fermion ground-state wave function, raised to an arbitrary power λ. For other permutations of the particles, we use the particle statistics—boson or fermion—to construct the wave function. This prescription works equally well on the continuum line of length L or on the discrete lattice of size N. The theory of random matrices singles out the ‘‘special’’ values of λ=1/2, 1, and 2, and provides techniques for calculating all correlations. Results obtained in this work include analytic expressions for the lattice momentum distributions, accurate numerical results for all momentum distributions and their critical exponents, and explicit results for the lattice pair-correlation functions. We emphasize that this is only for the stated special values of λ. Finally, these wave functions are evaluated as candidates for variational wave functions.