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Acta Physica Sinica

ELECTRON CORRELATION EFFECT IN THE HUBBARD-HIRSCH MODEL

Guozhu Wei, 东北大学物理系

Published Jan 1, 1994• 0 citations
Publisher

Abstract

Based on the single-site electron correlation, the local approach has been used to investigate the ferromagnetic phase in the Hubbard-Hirsch model. Using the R =0,α approximation in second-order calculation, the electron Correlation effect on the phase diagram has been studied Carefully. Comparing with those of the R=0 approximation, the electron correlation effect becomes weaker due to taking into aceount the nondiagonal elements of density matrix.

DOI
10.7498/aps.43.1828

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Based on the single-site electron correlation, the local approach has been used to investigate the ferromagnetic phase in the Hubbard-Hirsch model. Using the R =0,α approximation in second-order calculation, the electron Correlation effect on the phase diagram has been studied Carefully. Comparing with those of the R=0 approximation, the electron correlation effect becomes weaker due to taking into aceount the nondiagonal elements of density matrix.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons.The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high -Tc superconductivity, band magnetism and the metal-insulator transition.This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations.In this research the t -U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniques This research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems.We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established.It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high – Tc superconductivity, band magnetism and the metal-insulator transition. This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations. In this research the t – U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniquesThis research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems. We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established. It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine ferromagnetism in the one-dimensional Hubbard model with long-range and correlated hopping. It is found that the correlated hopping term stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n. The critical value of the interaction strength Uc above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is presented for physically the most interesting cases. 1 The Hubbard model has become, since its inception [1] in 1963, one of the most popular examples of a system of interacting electrons with short-range interactions. It has been used in the literature to study a great variety of many-body effects in metals, of which ferromagnetism, metal-insulator transitions, charge-density waves and superconductivity are the most common examples. Of all these cooperative phenomena the problem of ferromagnetism in the Hubbard model has the longest
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.