Physics of Particles and Nuclei

Diagrammatic analysis of the Hubbard model: Stationary property of the thermodynamic potential

V. A. Moskalenko, Leonid Alekseevich Dohotaru

Published Nov 25, 2010• 0 citations

Abstract

Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential, one-particle propagator and correlation function is established. This relation contains additional integration of the one-particle propagator by the auxiliary constant. The vacuum skeleton diagrams constructed from irreducible Green’s functions and tunneling propagator lines are determined and special functional is introduced. The properties of such functional are investigated and its relation to the thermodynamic potential is established. The stationary properties of this functional with respect to first order changing of the correlation function is demonstrated and as a consequence the stationary properties of the thermodynamic potential is proved.

DOI: 10.1134/s1063779610070130

Related papers

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

V. A. Moskalenko, Leonid Alekseevich Dohotaru, I. D. Cebotari

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.

arXiv:1001.1647Journal of Experimental and Theoretical PhysicsJul 1, 20102 citations

Stationary property of the thermodynamic potential of the Hubbard model in strong coupling diagrammatic approach for superconducting state

V. A. Moskalenko, Leonid Alekseevich Dohotaru, D. F. Digor +1 more

Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible Green's function of the superconducting state. As in the previous paper we introduce the notion of tunneling Green's function and of its mass operator. This last quantity turns out to be equal to correlation function of the system. We proved the existence of exact relation between renormalized one-particle propagator and thermodynamic potential which includes integration over auxiliary interaction constant. The notion of skeleton diagrams of propagator and vacuum kinds were introduced. These diagrams are constructed from irreducible Green's functions and tunneling lines. Identity of this functional to the thermodynamic potential has been proved and the stationarity with respect to variation of the mass operator has been demonstrated.

Low Temperature PhysicsOct 1, 20120 citations

Diagrammatic analysis of the Hubbard model II: Superconducting state

V. A. Moskalenko, Leonid Alekseevich Dohotaru, D. F. Digor +1 more

Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible Green's function of the superconducting state. As in the previous paper we introduce the notion of tunneling Green's function and of its mass operator. This last quantity turns out to be equal to correlation function of the system. We proved the existence of exact relation between renormalized one-particle propagator and thermodynamic potential which includes integration over auxiliary interaction constant. The notion of skeleton diagrams of propagator and vacuum kinds were introduced. These diagrams are constructed from irreducible Green's functions and tunneling lines. Identity of this functional to the thermodynamic potential has been proved and the stationarity with respect to variation of the mass operator has been demonstrated.

arXiv:1001.3325Jan 19, 20100 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.

arXiv:0804.1651Theoretical and Mathematical PhysicsApr 1, 20098 citations

DIAGRAM TECHNIQUE FOR THE HUBBARD MODEL. LADDER DIAGRAM SUMMATION

V. A. Moskalenko, L.Z. Kon

A new diagram technique based on the generalized Wick theorem has been elaborated for the systems with strong electronic correlations.Coulomb repulsion of the electrons of the Hubbard model is considered as the main part of Hamiltonian and is taken into account in a zero order approximation.The hopping matrix elements are considered as a perturbation.One-particle Matsubara-Green function of the model has been investigated and Dyson equation has been obtained.New elements of the theory which are characteristic of this new approach are the local many-particle irreducible Green functions, or Kubo cumulants.They become zero when Coulomb interaction is zero.The main task of this paper is the summing of ladder diagrams which take into account the most essential charge and spin fluctuations of the system.The integral equations, which sum such diagrams, have been established for two different channels.The coherent potential approximation has been used to simplify and solve these equations.On this basis a metal-dielectric phase transition has been investigated.

Condensed Matter PhysicsJan 1, 199812 citations

Dynamics and thermodynamics of the pseudospin-electron model in the case of absence of the electron Hubbard correlation. I. The analytical consideration

Ihor V. Stasyuk, Andrij M. Shvaika, K. V. Tabunschyk

Dynamics and thermodynamics of the model with local anharmonism in the case of absence of the electron (Hubbard) correlation is investigated in the present work. The correlation functions, mean values of pseudospin and particle number as well as the thermodynamical potential are calculated. The calculation is performed by diagrammatic method in the mean field approximation. Single--particle Green functions are taken in the Hubbard--I approximation.

arXiv:cond-mat/9811019Nov 2, 19980 citations