Cluster dynamical mean field theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean-field theory, periodized cluster dynamical mean-field theory (PCDMFT), is presented. The semiclassical limit of the cluster methods is analyzed by applying them to the Falikov-Kimball model in the limit of infinite Hubbard interaction U where they map to different classical cluster schemes for the Ising model. Furthermore, the Cutkosky-t'Hooft-Veltman cutting equations are generalized and derived for nontranslation invariant systems using the Schwinger-Keldysh formalism. This provides a general setting to discuss causality properties of cluster methods. To illustrate the method, we prove that PCDMFT is causal while the nested cluster schemes in general and the pair scheme in particular are not. Constraints on further extension of these schemes are discussed.Cluster dynamical mean field theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean-field theory, periodized cluster dynamical mean-field theory (PCDMFT), is presented. The semiclassical limit of the cluster methods is analyzed by applying them to the Falikov-Kimball model in the limit of infinite Hubbard interaction U where they map to different classical cluster schemes for the Ising model. Furthermore, the Cutkosky-t'Hooft-Veltman cutting equations are generalized and derived for nontranslation invariant systems using the Schwinger-Keldysh formalism. This provides a general setting to discuss causality properties of cluster methods. To illustrate the method, we prove that PCDMFT is causal while the nested cluster schemes in general and the pair scheme in particular are not. Constraints on further extension of these schemes are discussed.

arXiv:cond-mat/0307587Physical Review BMay 28, 200467 citations

Dynamical Mean Field Theory

Yoshio Kuramoto

Lecture notes in physicsJan 1, 20200 citations

Coupled-cluster impurity solvers for dynamical mean-field theory

Tianyu Zhu, Carlos A. Jiménez-Hoyos, James D. McClain +2 more

We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest that coupled-cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest that coupled-cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.

arXiv:1905.12050Physical review. B./Physical review. BSep 26, 201957 citations

Dynamical Mean-Field Theory

Dieter Vollhardt, Krzysztof Byczuk, Marcus Kollar

arXiv:1109.4833Springer series in solid-state sciencesAug 9, 201118 citations

Dynamical Mean-Field Theory

WORLD SCIENTIFIC eBooksMar 23, 20250 citations

A linear in

\beta

solver for Cluster Dynamical Mean Field Theory

U/t

and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest that coupled-cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.