Using equations of motion of connected Green functions the Hubbard III approximation is reexamined. It is shown that two important higher-order correlation effects are neglected in the Hubbard III treatment. One is bandwidth correction, the other is band-shift correction. These two corrections make important effects to the metal-insulator transition and spontaneous ferromagnetism in the Hubbard model. Due to the bandwidth correction the critical value of ${U}_{c}$ in the metal-insulator transition decreases from $\sqrt{3}/2W(W$ represents Bloch bandwidth) in the Hubbard III approximation to $0.67W,$ which approaches significantly the critical value of $0.5W$ by the quantum Monte Carlo simulation, while the band-shift correction leads to a ferromagnetic solution missed in the Hubbard III approximation in the limit of $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty},$ which is in qualitative agreement with the conclusion that the Hubbard model can describe the ferromagnetism resulted from the spectral density method and the quantum Monte Carlo simulation. Our studies show that the higher-order correlation effects play an important role in describing the properties of the strongly correlated systems.Using equations of motion of connected Green functions the Hubbard III approximation is reexamined. It is shown that two important higher-order correlation effects are neglected in the Hubbard III treatment. One is bandwidth correction, the other is band-shift correction. These two corrections make important effects to the metal-insulator transition and spontaneous ferromagnetism in the Hubbard model. Due to the bandwidth correction the critical value of ${U}_{c}$ in the metal-insulator transition decreases from $\sqrt{3}/2W(W$ represents Bloch bandwidth) in the Hubbard III approximation to $0.67W,$ which approaches significantly the critical value of $0.5W$ by the quantum Monte Carlo simulation, while the band-shift correction leads to a ferromagnetic solution missed in the Hubbard III approximation in the limit of $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty},$ which is in qualitative agreement with the conclusion that the Hubbard model can describe the ferromagnetism resulted from the spectral density method and the quantum Monte Carlo simulation. Our studies show that the higher-order correlation effects play an important role in describing the properties of the strongly correlated systems.

Physical review. B, Condensed matterFeb 15, 200011 citations

New Green function approach describing the ferromagnetic state in the simple Hubbard model

Grzegorz Górski, Jerzy Mizia, Krzysztof Kucab

We consider a Hubbard model with occupation dependent hopping integrals. Using the Hartree-Fock (H-F) approximation and the new Green function approach with inter-site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k-dependent spectral weights is included. In addition we obtain the shift of the spin bands which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT-Quantum Monte Carlo calculations and with the Hubbard III approximation which includes the correlated hopping effect.We consider a Hubbard model with occupation dependent hopping integrals. Using the Hartree-Fock (H-F) approximation and the new Green function approach with inter-site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k-dependent spectral weights is included. In addition we obtain the shift of the spin bands which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT-Quantum Monte Carlo calculations and with the Hubbard III approximation which includes the correlated hopping effect.

arXiv:1312.3150Dec 11, 20130 citations

New Green's function approach describing the ferromagnetic state in the Hubbard model with correlated hopping

Grzegorz Górski, Jerzy Mizia, Krzysztof Kucab

We consider a Hubbard model (HM) with occupation dependent hopping integrals. Using the Hartree–Fock (H–F) approximation and the new Green's function approach with inter‐site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k‐dependent spectral weights is included. In addition, we obtain the shift of the spin bands, which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model, the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT‐Quantum Monte Carlo calculations and with the Hubbard III approximation, which includes the correlated hopping effect.We consider a Hubbard model (HM) with occupation dependent hopping integrals. Using the Hartree–Fock (H–F) approximation and the new Green's function approach with inter‐site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k‐dependent spectral weights is included. In addition, we obtain the shift of the spin bands, which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model, the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT‐Quantum Monte Carlo calculations and with the Hubbard III approximation, which includes the correlated hopping effect.

physica status solidi (b)Jul 11, 20144 citations

Hubbard model and the origin of ferromagnetism

Hal Tasaki

The European Physical Journal BMar 18, 200862 citations

{U}_{c}

in the metal-insulator transition decreases from

\sqrt{3}/2W(W

represents Bloch bandwidth) in the Hubbard III approximation to

0.67W,

which approaches significantly the critical value of

0.5W

by the quantum Monte Carlo simulation, while the band-shift correction leads to a ferromagnetic solution missed in the Hubbard III approximation in the limit of $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty},$ which is in qualitative agreement with the conclusion that the Hubbard model can describe the ferromagnetism resulted from the spectral density method and the quantum Monte Carlo simulation. Our studies show that the higher-order correlation effects play an important role in describing the properties of the strongly correlated systems.