Onset of magnetization in the one-dimensional Fermi gas with attractive [formula omitted]-function potential

Abstract

The magnetic field dependence of the ground state of the one-dimensional spin-1/2 Fermi gas is studied with emphasis on the onset of the magnetization. The Bethe Ansatz solution shows that the system has three phases, namely, spin–singlet bound states (preformed Cooper pairs), spin-polarized particles and a mixed phase of the above. For small fields the ground state consists of paired states. At the critical field the band of unpaired (spin-up) particles starts to get gradually populated following the square-root dependence of the van Hove singularity of the empty parabolic band. The filled unpaired states correspond to the rapidity interval −B0≤k≤B0. We show that the square of the magnetization and B02 are initially linear in the field. For the case of spin-3/2 the Bethe Ansatz solution for the ground state has four fundamental bands: The particles can be either unpaired or bound in states of two, three and four fermions. The onset of the population of the first three bands again follows the square-root dependence of the one-dimensional van Hove singularity of the respective band. Our results are compared with previous studies where the magnetization is linear in the field.