Electron Correlations in Narrow Energy Bands: Ground State Energy and Metal-Insulator Transition

Abstract

The electron correlations in narrow energy bands are examined within the framework of the Hubbard model. The single-particle Green function and energy spectrum are obtained in a paramagnetic state at half-filling by means of a new two-pole approximation. Analytical expressions for the energy gap, polar states concentration and energy of the system are found in the ground state. Metal-insulator transitions in the model at the change of bandwidth or temperature are investigated. The results obtained are used for interpretation of some experimental data in narrow-band materials.

Energy spectrum of the organic quasi-1D conductors with NNN and correlated hopping

“…This approach gives a correct description of metal-insulator transition [20] in the Hubbard model (in particular, the calculated concentration of polar states is in accordance with the results of DMFT [8]) and reproduces the exact results [41,33] found for the partial case of the model with correlated hopping of electrons. For the exchange terms we apply the mean-field approximation:…”

“…The newly elaborated methods, in their turn, have their own deficiencies connected with greatly increased computation time, limitations on model parameters and difficulties with identifying the mechanisms of physical effects. At the same time, there exists a non-perturbative method [17,18] which permits to explain such peculiarities of strongly correlated electron systems as metal-insulator transition [19,20], electron-hole asymmetry of ferromagnetism [21,22], conductivity [23], etc. Moreover, this method permits to take into account the correlated hopping and indirect exchange interactions, important for real strongly correlated electron systems.…”

On strongly correlated electrons in metals

“…(5) apply for d > 1, T > 0, as seen below. Noteworthy is that none of the numerous numerical approximations 8,24 has achieved the remarkable agreement, displayed in Fig. 1.…”