Magnetic crossover in the one-dimensional Hubbard model in the presence ofa magnetic field

The ground-state (GS) properties of the one-dimensional (1D) Hubbard model at half-filling are examined in the presence of a magnetic field using the generalized mean-field (GMF) approach, which includes the spin-density and the electron-hole correlations on an equal footing. The GMF formalism provi des insight into both the metal-insulator transition and the transition fro m itinerant to localized magnetism with applied field. The GMF theory can d ifferentiate the energy gap from the antiferromagnetic order parameter in t he presence of a magnetic field. The numerical results for the GS energy, t he magnetization, the spin susceptibility, and the number of doubly occupie d sites are in good agreement with the exact results over a wide range of U /t and h/t. The calculated h-U phase diagram exhibits a magnetic crossover from itinerant electron-hole pairs to a Bose-Einstein condensate state of l ocal pairs. The overall picture of the magnetic crossover in ID is found to be similar for the simple case of constant density of states, putting the GMF approach on a firmer basis in two and three dimensions.