# Gutzwiller wave function/historical note

The Hubbard model expresses the fact that electrons in a crystal can tunnel from one atom to another and that deviations from the atoms' average charge are energetically unfavorable.

The importance of these charge fluctuations for the electron transport was recognized long before the official invention' of the Hubbard model. For example, de Boer and Verwey (1937), supported by Peierls (1937), pointed out that the electrostatic interaction energy between the 3d-electrons in nickel-oxide (NiO) is so large that the electrons will not move through the system, i.e., the electrical conductivity is zero. Therefore, NiO is an insulator despite the fact that the electronic bands are partially filled which would imply a metallic conductivity according to the Bloch-Wilson band theory. The concept of an insulating behavior due to the electron-electron interaction was worked out in more detail by Mott (1949), and insulators such as NiO are called Mott insulators'.

Anderson (1959) wrote down the electronic Hamiltonian in the Wannier basis from which he derived the antiferromagnetic Heisenberg exchange interaction in Mott insulators in the strong-coupling limit. Albeit this work contained all the elements needed to write down the (single-band) Hubbard model, it was not before 1963 that the Hamiltonian was independently introduced and published by Gutzwiller, Hubbard, and Kanamori, who aimed at an understanding of ferromagnetism in transition metals. Hubbard submitted his paper seven months later than Gutzwiller, and Hubbard's work was published three months later than Gutzwiller's article. For a collection of papers on the Hubbard model, see Montorsi (1992).