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physica status solidi (b)

Correlation Effects of the Antiferromagnetic Phase in the Hubbard Model

G. Z. Wel, H. Q. Nie, K. Y. Zhang

Published Nov 1, 1989• 4 citations
Publisher

Abstract

Abstract Using series expansion of local approach, the electron coupling between nearest‐neighbour sites is considered to investigate the electron correlation effect in the Hubbard model. The results show that when the off‐diagonal elements of the density matrix are considered in the calculation, it leads to an enhancement of double occupancy and are duce of the formation of the local moments.

DOI
10.1002/pssb.2221560137

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•Jan 1, 1994•2 citations
Abstract Using series expansion of local approach, the electron coupling between nearest‐neighbour sites is considered to investigate the electron correlation effect in the Hubbard model. The results show that when the off‐diagonal elements of the density matrix are considered in the calculation, it leads to an enhancement of double occupancy and are duce of the formation of the local moments.
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.
Using the local approach, we have performed a third·order perturbation calculation to investigate the effects of intra-atomic electron correlation and electron and spin correlation between nearest neighbour sites in the extended Hubbard model. We found that significant correction of the third order over the second order results and, in comparison with the results of the third-order perturbation where only the intra-atomic electron correlation is included, the influence of the electron and spin correlation between nearest neighbour sites on the correlation energy is non-negligible.
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.
We show that in the translation invariant case and in the antiferromagnetic phase, the reduced density matrix ρ2 has no off-diagonal long-range order of on-site electron pairs for the single-band Hubbard model on a cubic lattice away from half filling at finite temperatures both for the positive coupling and for the negative coupling. In these cases the model can not give a mechanism for the superconductivity caused by the condensation of on-site electron pairs and the nearestneighbor electron pairs. PACS numbers: 71.10.+x, 74.20.-z, 05.30.-d. 1 It was proposed the possibility that the Hubbard model can give a mechanism to characterize high temperature superconductivity[1]. It has been shown that the η pairing states for the single band Hubbard model with constant hopping matrix element for nearest neighbor sites have ODLRO[2]. It has also been shown that in the ground state the model with negative coupling has off-diagonal long-range order (ODLRO) on some bipartite lattice[3]. However, as the temperature T> 0 whether the reduced density matrix ρ2 has ODLRO is inconclusive. The purpose of this work is to study the ODLRO of ρ2 in the single-band Hubbard model with constant hopping matrix element for nearest neighbor pairs on a cubic lattice at finite temperatures. In the translation invariant case we obtain an equation ( (10) in the following) which is satisfied by the long-range correlation functions of on-site electron pairs. From which we find that there is no ODLRO of on-site electron pairs. Then we consider the case with an antiferromagnetic background. In this case we will show that there is still no ODLRO of on-site electron pairs. The Hamiltonian of the model is H = −t ∑ (a † rar ′ + b † rb ∑