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

Abstract

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 1D 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.

Holon-doublon binding as the mechanism for the Mott transition

“…As in several previous works [6,26,31,42] we approximate the ground state of the collective HD pair state with a BCStype wave function, representing the coherent superposition of bound HD pairs,…”

Exact and Self-Consistent Results in One-Dimensional Repulsive Hubbard Model

“…The exact gap increases with U/t and h, 35 while the GSCF gap increases with U/t and is a non-monotonous function of h. 45 Although the GSCF theory overestimates the exact gap everywhere, it still correctly displays the separation between the spin (∆ (+) π ) and charge (E (+) gap ) degrees of freedom for h cross ≤ h ≤ h sat .…”

“…Exactly at half-filling we studied the electron-hole (exciton) BCS-like pairing and magnetic crossover from itinerant into Bose-Einstein condensation regime driven by U/t and h. 45 In the Mott-Hubbard insulator, the quasi-particle energy gap undergoes transformation in the momentum space and the GSCF theory predict on the way to the saturated phase a certain distinction between the magnetic ordering with well-developed (localized ) moments and weak band-like (itinerant) magnetism.…”

“…Such a weak singular behavior of the energy gap gives rise to the crossover from itinerant into the localized magnetic regime. 45 The critical magnetic field h cross for spin crossover is determined from (33) h cross = 4t − 2sU .…”