Hard-core bosonization of the one-dimensional t-J model

The one-dimensional t-J model Hamiltonian is realized by using hard-core boson operators. A simple algorithm written in Mathematica based on a differential realization of the hard-core bosons for finding exact solutions of the model is proposed. As a simple example, some low-lying excitation energies, the inverse compressibility, and the superconducting structure factors, as well as the particle and spin entanglement of a system with 8 sites are calculated. The results not only confirm the validity of the hard-core boson picture, but also indicate that a quantum phase transition near phase-separation at zero temperature can also be recognized by the particle and spin entanglement.