Magnetic crossover in the one-dimensional Hubbard model in the presence of a 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 provides insight into both the metal-insulator transition and the transition from itinerant to localized magnetism with applied field. The GMF theory can differentiate the energy gap from the antiferromagnetic order parameter in the presence of a magnetic field. The numerical results for the GS energy, the magnetization, the spin susceptibility, and the number of doubly occupied 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 local 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.