Landau Theory of the Mott Transition in the Fully Frustrated Hubbard Model in Infinite Dimensions

TL;DR

This paper employs a Landau free energy functional approach to analyze the Mott transition in a fully frustrated Hubbard model in infinite dimensions, linking lattice free energy to impurity models and clarifying the transition's nature.

Contribution

It introduces a Landau free energy framework for the Mott transition in the Hubbard model, providing new insights into the transition's character and its relation to impurity models.

Findings

The Mott insulator becomes unstable below a critical interaction U.

A narrow band forms near the Fermi energy at zero temperature.

The approach clarifies the transition's nature and its applicability to real materials.

Abstract

We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides a simple relation between the free energy of the lattice model and that of its local description in terms of an impurity model. The character of the Mott transition in infinite dimensions, (as reviewed by Georges Kotliar Krauth and Rozenberg, RMP 68, 1996, 13) follows simply from the form of the free energy functional and the physics of quantum impurity models. At zero temperature, below a critical value of the interaction U, a Mott insulator with a finite gap in the one particle spectrum, becomes unstable to the formation of a narrow band near the Fermi energy. Using the insights provided by the Landau approach we answer questions raised about the dynamical mean field solution of the Mott transition problem, and comment on its applicability to three dimensional transition metal oxides.