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Journal of Physics F Metal Physics

On the ferromagnetic phase transition in Hubbard model

François Brouers, Carlos Mauricio Chaves

Published Aug 1, 1977• 3 citations
Publisher

Abstract

The authors have derived the free-energy functional of an extended Hubbard model Hamiltonian with interatomic interactions. They have shown that as far as the ferromagnetic transition is concerned universality holds and that introducing a short-range interaction between neighbours yields the same free-energy functional as for the simple Hubbard model if irrelevant terms are discarded.

DOI
10.1088/0305-4608/7/8/004

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The authors have derived the free-energy functional of an extended Hubbard model Hamiltonian with interatomic interactions. They have shown that as far as the ferromagnetic transition is concerned universality holds and that introducing a short-range interaction between neighbours yields the same free-energy functional as for the simple Hubbard model if irrelevant terms are discarded.
We derive the free energy functional of an extended Hubbard model Hamiltonian with interatomic interactions. One has to solve a four coupled fields (two vectorial spin fields and two scalar charge fields) problem. Two are potentially soft (one spin and one charge field). We show that as far as the ferromagnetic transition is concerned, universality holds and that introducing a short range interaction between neighbours yields the same free energy functional as for the simple Hubbard model if irrelevant coupling terms are discarded. For the charge ordered transition we show using renormalization group theory arguments that the spin-charge coupling is irrelevant and that the coupling between the two charge fields can give rise to a first or second order transition depending on the details of the metallic band structure and the value of the interaction energy parameters.
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
The recently introduced concept of exact mean-field theories is applied to the extended simplified Hubbard model, which is a one-band extended Hubbard model (including nearest-neighbor interaction) where only the \ensuremath{\downarrow} electrons can hop. An exact mean-field Hamiltonian is derived for the model on a Bethe lattice in the limit of a large coordination number (Z\ensuremath{\rightarrow}\ensuremath{\infty}). The mean-field Hamiltonian is used to calculate the Green functions and the free energy at half-filling. This exact solution is analyzed analytically at small and large values of the on-site (U) and nearest-neighbor (V) interaction strengths. One finds that a phase transition occurs at sufficiently low temperatures for all U,V>0. The low-temperature phase is a charge-density wave for V>1/2U and a spin-density wave for V1/2U. Special attention is paid to (i) the critical temperature as a function of U and V, (ii) the order parameter as a function of temperature, and (iii) the density of states. The density of states shows that the low-temperature phase is an insulator for all U,V provided that V/U\ensuremath{\ne}1/2, while the high-temperature phase is a paramagnetic metal for all V if U2, and a paramagnetic insulator if U>2. Many detailed results are given.