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Acta Physica Sinica

LOCAL APPROACH FOR THE EXTENDED HUBBARD MODEL

NIE HUI-QUAN, Guozhu Wei, Kaiyi Zhang, 东北工学院物理系

Published Jan 1, 1988• 1 citation
Publisher

Abstract

In this paper, using the local approach, we calculated the correlation energy, the local moments and the polarisation around the local moments in paramagnetic phase up to second order in the extended Hubbard model. It is shown that the polarisation is always antiferro-magnetic for different values of W. The correlation energy increases with W increasing for n = 1 and large U. The local moments and the antiferromagnetic polarisation decrease with W increasing for fixed n and U. While the effect of W on both the local moments and the antiferromagnetic polarisation is not obvious for small n or for large U and n = 1.

DOI
10.7498/aps.37.720

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In this paper, using the local approach, we calculated the correlation energy, the local moments and the polarisation around the local moments in paramagnetic phase up to second order in the extended Hubbard model. It is shown that the polarisation is always antiferro-magnetic for different values of W. The correlation energy increases with W increasing for n = 1 and large U. The local moments and the antiferromagnetic polarisation decrease with W increasing for fixed n and U. While the effect of W on both the local moments and the antiferromagnetic polarisation is not obvious for small n or for large U and n = 1.
The local approach to electron correlation in the Hubbard model has been extended to include charge and spin correlations between nearest neighbours. Both these effects are particularly important near the half-filled band and further stabilise local moments. Polarisation induced by local moments is shown to be antiferromagnetic independently of the band filling. A considerable gain in energy connected with the formation of the polarisation cloud indicates that short-range order should exist also at relatively high temperatures.
Based on the intraatomic electron correlation and the interatomic electron and spin correlation, the local approach has been used to the Hubbard model. The term〈OOH〉which was neglected in the general calculation is retained in our calculation. Camparing our results with those of the general calculation, we find that when U is large, the effects of the term〈OOH〉in the paramagnetic phase can not be heglected for calculating the correlation energy, the ground state energy, the local moments and the antiferromagnetic polarization around the local moments. To estimate more accurately the electron correlation effects, one has to calculate to higher orders and check he convergency of the series.
The variational approach initiated by Gutzwiller is extended to include antiferromagnetism. A simplified assumption corresponding to that adopted by him is used in order to evaluate the ground state energy of the Hubbard model and to draw the phase diagram similar to those constructed by Penn on the basis of the Hartree-Fock approximation. It is found that the antiferromagnetic state in the phase diagram is restricted to a narrow region bounded by threshold values for both the coupling constant and electron density. For sufficiently large intraatomic repulsion paramagnetic state becomes more stable than antiferromagnetic state except for the case of one electron per site. The phase transition between paramagnetic and antiferromagnetic states is of first order and the coexistence of these two states with different density occurs.
The effect of correlation on the antiferromagnetic and paramagnetic phases of Hubbard's model of a half-filled narrow band are investigated using second-order perturbation theory. Employing the gap of the antiferromagnetic state as a variational parameter, it is shown that the increase of the bandwidth/potential-energy ratio leads to a phase transition into the paramagnetic state nearly where Mott has estimated it to occur. The convergence of the perturbation expansion is shown to be excellent at the transition.
We study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and U.