Self-energy-functional approach: Analytical results and the Mott-Hubbard transition

TL;DR

This paper applies the self-energy-functional approach to the Hubbard model to analytically and numerically study the Mott-Hubbard transition, providing a thermodynamically consistent mean-field approximation that reproduces the full phase diagram.

Contribution

It introduces a two-site approximation within the self-energy-functional approach that accurately captures the Mott transition's phase diagram, including the critical point, with analytical solutions at zero temperature.

Findings

Reproduces the complete phase diagram of the Mott transition.

Allows analytical calculation of the critical point at T=0.

Provides a thermodynamically consistent mean-field approximation.

Abstract

The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the ``linearized DMFT'' which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T=0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.