Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Germany
Corresponding author: a email@example.com
Revised: 3 November 2003
Published online: 23 December 2003
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.
PACS: 71.10.-w – Theories and models of many-electron systems / 71.15.-m – Methods of electronic structure calculations / 71.30.+h – Metal-insulator transitions and other electronic transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003