Dynamical Mean-Field Approximation and Cluster Methods for Correlated Electron Systems

Thomas Maier, Mark Jarrell, Thomas Pruschke +1 more

This article reviews quantum cluster theories, a set of approximations for infinite lattice models which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding mean-field approximation when the cluster size becomes 1. Although quantum cluster theories were originally developed to treat disordered systems, they have more recently been applied to the study of ordered and disordered correlated systems, which will be the focus of this review. After a brief historical review, the authors provide detailed derivations of three cluster formalisms: the cluster perturbation theory, the dynamical cluster approximation, and the cellular dynamical mean-field theory. They compare their advantages and review their applications to common models of correlated electron systems.

Tetsuro Saso, 哲郎 佐宗

Dai S. Hirashima, 平島 大

Giulio Biroli, Gabriel Kotliar

We develop, clarify, and test various aspects of cluster dynamical mean field methods using a soluble toy model as a benchmark. We find that the cellular dynamical mean field theory (CDMFT) converges very rapidly and compare its convergence properties with those of the dynamical cluster approximation. We propose and test improved estimators for the lattice self-energy within CDMFT.

Karan Aryanpour, Thomas Maier, Mark Jarrell

We comment on the article by Biroli and Kotliar [Phys. Rev. B 65, 155112 (2002)] in which they make a comparison between two cluster techniques, the cellular dynamical mean field theory (CDMFT) and the dynamical cluster approximation (DCA). Based upon an incorrect implementation of the DCA technique in their work, they conclude that the CDMFT is a faster converging technique than the DCA. We present the correct DCA prescription for the particular model Hamiltonian studied in their article and conclude that the DCA, once implemented correctly, is a faster converging technique for the quantities averaged over the cluster.

S. Moukouri, Carey Huscroft, Mark Jarrell