Abstract
The ground-state (GS) properties of the one-dimensional (1D) Hubbardmodel at half-filling are examined in the presence of a magnetic fieldusing the generalized mean-field (GMF) approach, which includesthe spin-density and the electron-hole correlations on an equalfooting. The GMF formalism provides insight into both themetal-insulator transition and the transition from itinerant tolocalized magnetism with applied field. The GMF theory candifferentiate the energy gap from the antiferromagnetic orderparameter in the presence of a magnetic field. The numerical resultsfor the GS energy, the magnetization, the spin susceptibility, andthe number of doubly occupied sites are in good agreement with theexact results over a wide range of U/t and h/t. The calculatedh-U phase diagram exhibits a magnetic crossover from itinerantelectron-hole pairs to a Bose-Einstein condensate state of localpairs. The overall picture of the magnetic crossover in 1D is foundto be similar for the simple case of constant density of states,putting the GMF approach on a firmer basis in two and threedimensions.
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