Mott metal-insulator transition in the Hubbard model

TL;DR

This paper analyzes the Mott metal-insulator transition within the Hubbard model, emphasizing the roles of strong coupling, Kondo effects, and resonating-valence-bond states, and discusses limitations of the model in explaining actual transitions.

Contribution

It provides a detailed theoretical analysis of the Hubbard model's ground states and clarifies the conditions under which a Mott insulator or Fermi liquid state occurs, highlighting the need for additional effects to explain real transitions.

Findings

Normal Fermi liquid is stable in strong coupling for certain parameters.

Mott insulator occurs at half-filling with infinite U/W.

Actual metal-insulator transitions require effects beyond the Hubbard model.

Abstract

The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.