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

Correlation effects in the Hubbard model

Jakob Bernasconi

Physics of Condensed MatterJan 1, 19723 citations

Correlation effects in the Hubbard model

Jakob Bernasconi

The European Physical Journal BJul 1, 19725 citations

Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method

Louis Haurie, Maxence Grandadam, Emile Pangburn +3 more

Abstract We use the composite operator method (COM) to analyze the strongly correlated repulsive Hubbard model, investigating the effect of nearest-neighbor hoppings up to fourth order on a square lattice. We consider two sets of self-consistent equations, one enforcing the Pauli principle and the other imposing charge-charge, spin-spin, and pair–pair correlations using a decoupling scheme developed by Roth (1969 Phys. Rev. 184 451–9). We extract three distinct solutions from these equations: COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. An overview of the method studying the validity of particle-hole symmetry and the Luttinger theorem for each solution is presented. Additionally, we extend the initial basis to study superconductivity, concluding that it is induced by the Van Hove singularity. Finally, we include higher-order hoppings using realistic estimates for tight binding parameters and compare our results with ARPES measurements on cuprates.Abstract We use the composite operator method (COM) to analyze the strongly correlated repulsive Hubbard model, investigating the effect of nearest-neighbor hoppings up to fourth order on a square lattice. We consider two sets of self-consistent equations, one enforcing the Pauli principle and the other imposing charge-charge, spin-spin, and pair–pair correlations using a decoupling scheme developed by Roth (1969 Phys. Rev. 184 451–9). We extract three distinct solutions from these equations: COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. An overview of the method studying the validity of particle-hole symmetry and the Luttinger theorem for each solution is presented. Additionally, we extend the initial basis to study superconductivity, concluding that it is induced by the Van Hove singularity. Finally, we include higher-order hoppings using realistic estimates for tight binding parameters and compare our results with ARPES measurements on cuprates.

arXiv:2305.08591Journal of Physics Condensed MatterJan 12, 202410 citations

Functional-derivative study of the Hubbard model. I. Perturbation method and first-order approximation

Tadashi Arai, Morrel H. Cohen, Monica Tosi

In order to study the properties of the Hubbard model for narrow bands, a systematic treatment of the equations of motion of the Green's functions appropriate to that model has been developed. Higher-order Green's functions are reduced to functional derivatives of the basic Green's function $G$ and calculated iteratively in a perturbation scheme which takes the Hubbard I solution ${G}_{0}$ as the zeroth-order Green's function. A zeroth-order approximation to the self-energy correction obtained by inserting ${G}_{0}$ into the functional derivatives is compared with various existing solutions. The perturbation scheme is further extended to an infinite order and the self-energy is calculated exactly up to terms linear in the hopping motion $\ensuremath{\epsilon}$, a result which has not been obtained previously. The self-energy correction in this final result is drastically different from the zeroth-order solution, demonstrating the importance of the infinite-order iterative procedure. Finally, the electron correlations included in the final result are discussed in terms of diagrams.In order to study the properties of the Hubbard model for narrow bands, a systematic treatment of the equations of motion of the Green's functions appropriate to that model has been developed. Higher-order Green's functions are reduced to functional derivatives of the basic Green's function $G$ and calculated iteratively in a perturbation scheme which takes the Hubbard I solution ${G}_{0}$ as the zeroth-order Green's function. A zeroth-order approximation to the self-energy correction obtained by inserting ${G}_{0}$ into the functional derivatives is compared with various existing solutions. The perturbation scheme is further extended to an infinite order and the self-energy is calculated exactly up to terms linear in the hopping motion $\ensuremath{\epsilon}$, a result which has not been obtained previously. The self-energy correction in this final result is drastically different from the zeroth-order solution, demonstrating the importance of the infinite-order iterative procedure. Finally, the electron correlations included in the final result are discussed in terms of diagrams.

Physical review. B, Solid stateFeb 15, 19778 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.

G

and calculated iteratively in a perturbation scheme which takes the Hubbard I solution

{G}_{0}

as the zeroth-order Green's function. A zeroth-order approximation to the self-energy correction obtained by inserting

{G}_{0}

into the functional derivatives is compared with various existing solutions. The perturbation scheme is further extended to an infinite order and the self-energy is calculated exactly up to terms linear in the hopping motion $\ensuremath{\epsilon}$, a result which has not been obtained previously. The self-energy correction in this final result is drastically different from the zeroth-order solution, demonstrating the importance of the infinite-order iterative procedure. Finally, the electron correlations included in the final result are discussed in terms of diagrams.