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arXiv:cond-mat/9910068

On Chemical Potential of a Generalized Hubbard Model with Correlated Hopping at Half-Filling

L. Didukh, V. Hankevych

Published Oct 6, 1999• 0 citations
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Abstract

In the present paper we study chemical potential of a generalized Hubbard model with correlated hopping at half-filling using a generalized mean-field approximation. For the special case of the model the approach reproduces the exact results: metal-insulator transition, ground state energy. Chemical potential of generelized Hubbard model with correlated hoppig as function of hopping integrals at zero temperature is found. It is shown that chemical potential of the model is temperature-dependent. The dependences of chemical potential of a generalized Hubbard model with correlated hopping on the model parameters are different in metallic and insulating phases leading to a kink at the point of metal-insulator transition in the ground state. With the increase of temperature the kink in the chemical potential curve disappears. The obtained results differ from those of the Hubbard model indicating the important role of correlated hopping.

DOI
10.48550/arxiv.cond-mat/9910068

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In the present paper we study chemical potential of a generalized Hubbard model with correlated hopping at half-filling using a generalized mean-field approximation. For the special case of the model the approach reproduces the exact results: metal-insulator transition, ground state energy. Chemical potential of generelized Hubbard model with correlated hoppig as function of hopping integrals at zero temperature is found. It is shown that chemical potential of the model is temperature-dependent. The dependences of chemical potential of a generalized Hubbard model with correlated hopping on the model parameters are different in metallic and insulating phases leading to a kink at the point of metal-insulator transition in the ground state. With the increase of temperature the kink in the chemical potential curve disappears. The obtained results differ from those of the Hubbard model indicating the important role of correlated hopping.
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.
We study the metal-insulator transition of the d-dimensional Hubbard model by treating the hopping term between adjacent 1-d chains in the frame of a Clifford linearization scheme, and keeping the full model along the chains. A general equation for the critical point is worked out in terms of the correlation functions of the one-dimensional model, assuming that the transition is of the second order. The equation, which holds at any temperature, is here investigated especially at T=0, where the latter condition holds true. The solution shows the existence of an insulating ground state in any d only at half-filling for U strictly positive, as in the exact 1-d case. The transition is found to be related to a parameter reminiscent of entropy.
In the present paper we study chemical potential of the generalized Hubbard model with correlated hopping. The peculiarity of the model in comparison with similar generalized Hubbard models is the concentration dependence of hopping integrals. Chemical potential as a function of the model energy parameters, electron concentration and temperature is found. It is shown that correlated hopping and temperature changes essentially the chemical potential location; these dependencies differ strongly at different values of the electron concenntration.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that in the half-filled band case the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition. Outside half-filling correlated hopping stabilizes the segregated phase in the ground-state, however, the nature of the ground-state remains qualitatively unchanged.
We have applied mean-field theory to calculate the spin-density-wave (SDW) order parameter \ensuremath{\Delta}, the chemical potential \ensuremath{\mu}, and the ground-state energy at various band fillings for the Hubbard model. We have found that at zero temperature and in the large-U limit, the SDW order parameter and the ground-state energy can be written as \ensuremath{\Delta}=U(1-x)/2-O(J) and Eg{\mathit{E}}_{\mathit{g}}Eg​=-U(1-x)2{)}^{2})2/4-0(J). The chemical potential obtained here for x=0 and 1 agrees well with the result obtained by the exact-diagonalization calculation on a 4\ifmmode\times\else\texttimes\fi{}4 sites cluster by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)]. In the SDW phase, the mean-field theory gives an upward shift in the chemical potential as one dopes away from half-filling, which is in contrast with the exact-diagonalization calculations. This result indicates that the Mott-Hubbard gap is depressed much more rapidly in the mean-field theory than the exact-diagonalization calculation. The doping dependence of ground-state energy calculated here is in good agreement with the above numerical calculation for doping up to 0.5. Here, U is the intrasite Coulomb repulsion, x is doping concentration, J=4t2{\mathit{t}}^{2}t2/U is the superexchange interaction parameter, and t is the hopping integral for the nearest neighbors.