Ground state properties of one-dimensional Bose-Fermi mixtures

Bose-Fermi mixtures in one dimension are studied in detail on the basis of an exact solution. Corresponding to three possible choices of the referecce state in the quantum inverse scattering method, three sets of Bethe-ansatz equations are derived explicitly. The features of the ground state and low-lying excitations are investigated. The ground state phase diagram caused by the external field and chemical potential is obtained.