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International Journal of Modern Physics B

ENERGY GAP IN THE HUBBARD MODEL

L. Didukh, Yu. Dovhopyaty, Yuriy Skorenkyy

Published Mar 20, 2000• 0 citations
Publisher

Abstract

A new variant of the generalized Hartree–Fock approximation for calculation of single-particle Green function in the Hubbard model is proposed. The calculated single-particle energy spectrum allows to study metal–insulator transition. Dependences of the energy gap width and the polar states concentration on model parameters are obtained. Conditions of a metallic and an insulating state realisation are found.

DOI
10.1142/s0217979200000613

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A new variant of the generalized Hartree–Fock approximation for calculation of single-particle Green function in the Hubbard model is proposed. The calculated single-particle energy spectrum allows to study metal–insulator transition. Dependences of the energy gap width and the polar states concentration on model parameters are obtained. Conditions of a metallic and an insulating state realisation are found.
A new two-pole approximation, which allows to describe the transition from an insulating state to a metallic one at increase of bandwidth, and also the observable in some compounds transition from a metalic state to an insulating one with increasing temperature, is presented. The case of a paramagnetic narrow-band material at half-filling is considered. Single-particle Green function and energy spectrum of electron system are calculated. The expressions for energy gap width and the concentration of polar states (holes or doublons) are obtained. The conditions for metallic and insulating states are found.
For the one-dimensional Hubbard model we extended the bosonization technique, away from half-filling, in such a way that a general formula is obtained for the zero temperature single-particle Green function with validity over the whole doping range. Our method allows us to calculate, for the first time, the one-body Green function in both Tomonaga-Luttinger and Luther-Emery universality classes, to characterize the crossover between these two behaviors and thus, to describe the metal-insulator transition. We have found that the transition can be characterized as a Brinkman-Rice transition with a diverging effective mass.
A generalized Hubbard model with correlated hoppings is studied at half filling using exact diagonalization methods. For certain values of the hopping parameters our results for several static properties, the Drude weight and the single-particle spectra function, suggest the occurrence of a metal-insulator transition (MIT) at a finite value of the local Coulomb interaction Uc{\mathit{U}}_{\mathit{c}}Uc​. We identify the regions of the hopping parameters where the MIT is of the Mott type. In these regions, for large UUc{\mathit{U}}_{\mathit{c}}Uc​, we find a ferromagnetic ground state.
A new non-perturbative framework for many-body correlated systems is formulated by extending the operator projection method (OPM). This method offers a systematic expansion which enables us to project into the low-energy structure after extracting the higher-energy hierarchy. This method also opens a way to systematically take into account the effects of collective excitations. The Mott-Hubbard metal-insulator transition in the Hubbard model is studied by means of this projection beyond the second order by taking into account magnetic and charge fluctuations in the presence of the high-energy Mott-Hubbard structure. At half filling, the Mott-Hubbard gap is correctly eproduced between the separated two bands. Near half filling, a strongly renormalized low-energy single-particle excitations coexisting with the Mott-Hubbard bands are shown to appear. Signifcance of momentum-dependent self-energy in the results is stressed.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.