Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Abstract

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-1 range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We also present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High Tc Cuprates

“…Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using dynamical mean field theory (DMFT) 21) with two kinds of impurity solvers : iterated perturbation theory (IPT) [22][23][24][25][26][27][28][29] and continuous time quantum Monte Carlo (CT-QMC) [30][31][32][33][34][35] We find that the electron-hole asymmetry can exist even under common interaction strengths between the hole-and the electron-doped systems. The asymmetry of the spectrum already exists in the non-interacting case, but it is drastically enhanced, especially when the interaction is strong enough to make the non-doped case a Mott insulator.…”

Superfluid to Mott-Insulator Transition in Bose-Hubbard Models

“…More specifically, the data suggest that, especially in threedimensions, a Mott-Hubbard gap of order U develops already on the superfluid side of the MIT, akin to what is predicted to occur in electronic systems. [4] Although these evidences are not incompatible with the accepted theory of the critical behavior across the superfluid-toinsulator transition, [5] they clearly demand for a more detailed comprehension that must include also highenergy excitations. There have been already several theoretical attempts, mainly based on suitable extensions of mean-field theory, to uncover the whole dynamical behavior across the MIT.…”

Hole-s± State Induced by Coexisting Ferro- and Antiferromagnetic and Antiferro-orbital Fluctuations in Iron Pnictides

“…(4) is measured by means of continued fraction algorithm. 29 It includes automatically all vertex corrections respect to theχ 0 (iω n ), without the need of explicit calculation of the local irreducible vertex function. The effective pairing interaction for the spin-singlet state, obtained by using the spin (charge-orbital) susceptibility in eq.…”