EXACT AND SELF-CONSISTENT RESULTS IN ONE-DIMENSIONAL REPULSIVE HUBBARD MODEL

Abstract

The shortcomings and advantages of the generalized self-consistent field (GSCF) approach, which includes the electron–hole order parameter [Formula: see text] and the average spin s within the one-dimensional repulsive Hubbard model, are analyzed by comparison of the ground state properties with the corresponding Bethe ansatz results in an entire parameter space of interaction strength U/t ≥ 0, magnetic field h ≥ 0 and electron concentration 0 ≤ n ≤ 1. The GSCF spectral characteristics are derived and criteria are found for the stability of incommensurate magnetic phase with the wave number 0 < q < π. The GSCF theory displays a simple relationship for the double occupancy D(+) in terms of n, s and [Formula: see text], where D(+) underestimates electron correlations at weak and intermediate ranges and overestimates correlations at large interaction strengths. Beyond some critical U/t and n≠1 the GSCF D(+) for spatially homogeneous state vanishes, while the exact D for all n at h=0 decreases gradually as U/t increases. At n ≠ 1 the GSCF chemical potential μ(+) overestimates electron correlations everywhere and variation μ(+)versusn displays electron instability toward the phase separation in the vicinity of n=1. Exactly at n=1 the GSCF μ(+)versusU/t always underestimates electron correlation and as U/t → ∞ at h=0 we have μ(+) → 0, while the Bethe ansatz result gives μ → 2t. In the limiting cases U/t → 0 and U/t → ∞ for all h ≥ 0 and 0 ≤ n ≤ 1 the GSCF ground state energy is exact, which is necessary for formulation of converging perturbation procedure about mean field solution in the entire parameter space.