An exact sum-rule for the Hubbard model: an historical approach

Sergio Di Matteo (1) , Yann Claveau (2)

1 IPR - Institut de Physique de Rennes
2 IM2NP - Institut des Matériaux, de Microélectronique et des Nanosciences de Provence

The aim of the present article is to derive an exact integral equation for the Green function of the Hubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though our exact integral equation does not allow to solve the Hubbard model, it represents a strong constraint on its approximate solutions. An analogous sum rule has been already obtained in the literature, through the use of a spectral moment technique. We think however that our equation-of-motion procedure can be more easily related to the historical procedure of the original Hubbard papers. We also discuss examples of possible applications of the sum rule and propose and analyse a solution, fulfilling it, that can be used for a pedagogical introduction to the Mott-Hubbard metal-insulator transition.

Mots clés: hubbard model; green functions; mott metal-insulator transition

Domaines: Physique [physics]

Sergio Di Matteo, Yann Claveau. An exact sum-rule for the Hubbard model: an historical approach. European Journal of Physics, 2017, 38 (4), pp.045501. ⟨10.1088/1361-6404/aa6900⟩. ⟨hal-01532198⟩