Mean-field solution of the Hubbard model: the magnetic phase diagram

Yann Claveau (1) , Brice Arnaud (1) , Sergio Di Matteo (1)

1 IPR - Institut de Physique de Rennes

The present paper is based on our graduate lectures in condensed-matter physics. We found that the mean-field solution of the Hubbard model is an excellent tool to stimulate students' reflections towards the treatment of realistic magnetic interactions. We show by detailed analytical and numerical calculations how to find the mean-field solution of the model on a square lattice. We then interpret the physical implications of the ground-state magnetic phase diagram in terms of the electron density and the ratio between the Coulomb repulsion and the electron-structure bandwidth.

Mots clés: Condensed matter: electrical; magnetic and optical; Education and communication

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Yann Claveau, Brice Arnaud, Sergio Di Matteo. Mean-field solution of the Hubbard model: the magnetic phase diagram. European Journal of Physics, 2014, 35 (3), pp.035023. ⟨10.1088/0143-0807/35/3/035023⟩. ⟨hal-00980582⟩