The exact phase diagrams of the one-dimensional Hubbard model, both attractive and
repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n
and on-site interaction strengths U < 0 or U > 0 are calculated and investigated. The exact
ground-state properties, namely, the ground-state energy, the average spin (magnetization), the
concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin
(magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide
range of interaction strengths U for various h and n. It is found that the spin susceptibility at half-
filling is non-analytic and changes discontinuously asU → 0. The exact theory shows the absence
of a charge energy gap in the U 0 region for all n and provides, for the chemical potential,
the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical
results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in
full agreement with the numerical calculations.
關聯:
Journal of Physics Condensed Matter 12(33), pp.7433-7454
