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

Comment on “Solution of Classical Stochastic One-Dimensional Many-Body Systems”

Su‐Chan Park, Jeong-Man Park, Doochul Kim

In a recent Letter, Bares and Mobilia proposed the method to find solutions of the stochastic evolution operator $H=H_0 + {γ\over L} H_1$ with a non-trivial quartic term $H_1$ . They claim, ``Because of the conservation of probability, an analog of the Wick theorem applies and all multipoint correlation functions can be computed.'' Using the Wick theorem, they expressed the density correlation functions as solutions of a closed set of integro-differential equations. In this Comment, however, we show that applicability of Wick theorem is restricted to the case $γ= 0$ only.In a recent Letter, Bares and Mobilia proposed the method to find solutions of the stochastic evolution operator $H=H_0 + {γ\over L} H_1$ with a non-trivial quartic term $H_1$. They claim, ``Because of the conservation of probability, an analog of the Wick theorem applies and all multipoint correlation functions can be computed.'' Using the Wick theorem, they expressed the density correlation functions as solutions of a closed set of integro-differential equations. In this Comment, however, we show that applicability of Wick theorem is restricted to the case $γ= 0$ only.

arXiv:cond-mat/0008209Physical Review LettersJul 24, 20009 citations

Lectures on correlation functions

Alexander L. Fetter

Lecture notes in physicsJan 1, 19832 citations

In a recent Letter, Bares and Mobilia proposed the method to find solutions of the stochastic evolution operator

H=H_0 + {γ\over L} H_1

with a non-trivial quartic term

H_1

. They claim, ``Because of the conservation of probability, an analog of the Wick theorem applies and all multipoint correlation functions can be computed.'' Using the Wick theorem, they expressed the density correlation functions as solutions of a closed set of integro-differential equations. In this Comment, however, we show that applicability of Wick theorem is restricted to the case

γ= 0

only.