On chemical potential of a generalized Hubbard model with correlated hopping at half-filling

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: metalinsulator 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. 1 Model Hamiltonian One of the simplest model describing correlation effects in narrow energy bands is the Hubbard model [1]. The model Hamiltonian contains two energy parameters: the matrix element t0 being the hopping integral of an electron from one site to another (t0 is not dependent on occupation of sites involved in the hopping process) and the parameter U being the intra-atomic Coulomb repulsion of two electrons of the opposite spins. This model is studied intensively (for recent reviews see Refs. [2, 3]). Theoretical analyses, on the one hand, and available experimental data, on the other hand, point out the necessity of the Hubbard model generalization by taking into account correlated hopping. This necessity is caused by two reasons. Firstly, theoretical analyses [4, 5] point out the inapplicability of the Hubbard model for the description of real strongly correlated electron systems, in some compounds (e.g. see the estimation in Refs. [4, 6]-[9]) the matrix element of electron-electron interaction describing correlated hopping is the same order that the hopping integral or on-site Coulomb repulsion. Secondly, using the concept of correlated hopping and caused by it the electron-hole asymmetry we can interpret the peculiarities of some physical properties of narrow-band materials [4, 10]-[16]. Hirsch showed that in contrast to the hopping integral of the Hubbard model (which is not dependent on occupation of sites involved in the hopping process) this parameter of a generalized Hubbard model had to depend on occupation of sites involved in the hopping process. Hamiltonian of the generalized in such a way Hubbard model is written as H = − ∑ ijσ tσija + iσajσ + U ∑ i ni↑ni↓, (1.1) tσij = tAA(1− niσ̄)(1− njσ̄) + tAB(niσ̄ + njσ̄ − 2niσ̄njσ̄) + tBBniσ̄njσ̄. (1.2) In recent few years Hamiltonian (1.1) is widely used to study metal-insulator transition in narrow energy bands [17]-[19]. In Ref. [4, 15] the necessity of the Hubbard model generalization by taking into account the matrix element of electron-electron interaction describing intersite hoppings of electrons had been pointed out. The Hamiltonian of the generalized Hubbard model with correlated hopping is H = H0 +H1 +H ′ 1, (1.3) H0 = −μ ∑