Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Abstract

Abstract. 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 halffilling is non-analytic and changes discontinuously as U → 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.

Entanglement in many-body systems

“…The Hubbard model in a magnetic field was proved to exhibit two quantum critical points at h a± c = 4(|U | ± 1) and half filling for U < 0, while there is one at h r c = 4( √ t 2 + U 2 − U ) for U > 0 (Yang et al, 2000). If a nearest neighbor Coulomb repulsion V σ,σ ′ ,j n jσ n j+1σ ′ is taken into account in Eq.…”

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

“…The exact D (Appendix C) and GSCF D (+) (5) are compared 35,50 in Fig. 9 and we see that the GSCF approach becomes ineffective at weak and intermediate interaction U/t.…”

“…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 .…”

“…24 It is the lack of the exact solution in the thermodynamic limit in 2D case that puts the test of the most general linear mean field theory, using the Bethe ansatz theory, 25-33 on a firmer basis in the extreme conditions of one dimensionality. 14,34,35 Due to strong quantum disorder the universal mean-field scheme with continuous broken symmetry is traditionally considered inadequate for strongly correlated systems in 1D case. It is certainly true for long-range characteristics, while shortrange correlations can address some ground state properties quantitatively correct in wide range of U > 0 and U < 0 Hubbard model even in 1D case.…”

“…(30) is close to the corresponding boundary between ferromagnetic and spiral phases in 1D Kondo model with renormalized parameter J c = 2U homog πn. 52,53 In the Bethe ansatz approach the critical magnetic field h sat of phase transition is given by the formula (U ≥ 0) 32,35,50 …”