We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as difficult to calculate as the original GF, and the Atomic Approximation consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. This approximation has already been used for the case of infinite electronic repulsion U (Phys. Rev. B 62, 7882 (2000)), and here we extend the treatment to the case of finite U. The method can also be applied to the single impurity Anderson model (SIAM), and we give explicit expressions of the approximate GF both for the PAM and the SIAM.We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as difficult to calculate as the original GF, and the Atomic Approximation consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. This approximation has already been used for the case of infinite electronic repulsion U (Phys. Rev. B 62, 7882 (2000)), and here we extend the treatment to the case of finite U. The method can also be applied to the single impurity Anderson model (SIAM), and we give explicit expressions of the approximate GF both for the PAM and the SIAM.

arXiv:0903.0139Mar 1, 20094 citations

Exact and approximate results for the Anderson impurity model

U. Brandt, Andreas Giesekus

The European Physical Journal BDec 1, 19891 citation

Anderson impurity model in the cumulant approach

G. Polatsek, K. W. Becker, Vilen Zevin

We discuss the ground-state energy of the Anderson degenerate impurity model for both finite and infinite on-site Coulomb repulsion U. The goal of the paper is to demonstrate the applicability of a theoretical approach to static ground-state properties introduced recently. This approach is based on the projection technique and on the introduction of cumulants. It allows for proper treatment of strong electronic correlations that are incorporated in the model. It also guarantees the size consistency of the evaluated physical quantities. We start from a compact expression for the ground-state energy, which is expanded into a continued fraction. By summing up the infrared divergencies, a self-consistent equation for the ground-state energy is found. For degeneracy ${\mathit{N}}_{\mathit{f}}$ \ensuremath{\rightarrow}\ensuremath{\infty} and U\ensuremath{\rightarrow}\ensuremath{\infty} the equation can be solved rigorously and gives the well-known Varma-Yafet solution. For ${\mathit{N}}_{\mathit{f}}$ and U both finite our procedure leads to the result of the variational approach of Gunnarsson and Sch\"onhammer.We discuss the ground-state energy of the Anderson degenerate impurity model for both finite and infinite on-site Coulomb repulsion U. The goal of the paper is to demonstrate the applicability of a theoretical approach to static ground-state properties introduced recently. This approach is based on the projection technique and on the introduction of cumulants. It allows for proper treatment of strong electronic correlations that are incorporated in the model. It also guarantees the size consistency of the evaluated physical quantities. We start from a compact expression for the ground-state energy, which is expanded into a continued fraction. By summing up the infrared divergencies, a self-consistent equation for the ground-state energy is found. For degeneracy ${\mathit{N}}_{\mathit{f}}$\ensuremath{\rightarrow}\ensuremath{\infty} and U\ensuremath{\rightarrow}\ensuremath{\infty} the equation can be solved rigorously and gives the well-known Varma-Yafet solution. For ${\mathit{N}}_{\mathit{f}}$ and U both finite our procedure leads to the result of the variational approach of Gunnarsson and Sch\"onhammer.

Physical review. B, Condensed matterSep 15, 19911 citation

Interpolation solution of the single-impurity Anderson model

A. L. Kuzemsky

Physics Letters AMar 1, 19918 citations

Multi-level Algorithm for the Anderson Impurity Model

Shailesh Chandrasekharan A, Jaebeom Yoo, Harold U. Baranger

APSMar 1, 20040 citations

Diagrammatic theory for the Anderson impurity model: Stationary property of the thermodynamic potential

V. A. Moskalenko, P. Entel, Leonid Alekseevich Dohotaru +1 more

We propose a diagrammatic theory around the atomic limit for the normal state of the Anderson impurity model. The new diagram method is based on Wick’s theorem for conduction electrons and a generalized Wick’s theorem for strongly correlated impurity electrons, which coincides with the definition of the Kubo cumulant. We prove a linked-cluster theorem for the mean of the evolution operator and obtain Dysontype equations for the one-particle propagators. The main element in these equations is the impurity electron correlation function, which contains the spin, charge, and pairing fluctuations of the system. We express the system thermodynamic potential in terms of the full propagator of conduction electrons and the correlation function. We establish that the thermodynamic potential is stationary under changes of the correlation function.We propose a diagrammatic theory around the atomic limit for the normal state of the Anderson impurity model. The new diagram method is based on Wick’s theorem for conduction electrons and a generalized Wick’s theorem for strongly correlated impurity electrons, which coincides with the definition of the Kubo cumulant. We prove a linked-cluster theorem for the mean of the evolution operator and obtain Dysontype equations for the one-particle propagators. The main element in these equations is the impurity electron correlation function, which contains the spin, charge, and pairing fluctuations of the system. We express the system thermodynamic potential in terms of the full propagator of conduction electrons and the correlation function. We establish that the thermodynamic potential is stationary under changes of the correlation function.

arXiv:0804.1651Theoretical and Mathematical PhysicsApr 1, 20098 citations

{\mathit{N}}_{\mathit{f}}

\ensuremath{\rightarrow}\ensuremath{\infty} and U\ensuremath{\rightarrow}\ensuremath{\infty} the equation can be solved rigorously and gives the well-known Varma-Yafet solution. For

{\mathit{N}}_{\mathit{f}}

and U both finite our procedure leads to the result of the variational approach of Gunnarsson and Sch\"onhammer.