scholarly journals Self-consistent Dyson equation and self-energy functionals: An analysis and illustration on the example of the Hubbard atom

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Walter Tarantino ◽  
Pina Romaniello ◽  
J. A. Berger ◽  
Lucia Reining
Keyword(s):  
Dyson Equation ◽  
Energy Functionals ◽  
Self Energy ◽  
Self Consistent

scholarly journals Self-Consistent Calculation of Particle-Hole Diagrams on the Matsubara Frequency: Flex Approximation

1997 ◽  
Vol 08 (05) ◽  
pp. 1145-1158
Author(s):  
J. J. Rodríguez-Núñez ◽  
S. Schafroth
Keyword(s):  
Hubbard Model ◽  
Imaginary Part ◽  
Chemical Potential ◽  
Order Approximation ◽  
The Self ◽  
Green Functions ◽  
Matsubara Frequency ◽  
Self Energy ◽  
Peak Structure ◽  
Self Consistent

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling (ρ =0.40), and for T/t = 0.03, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im Σ( k , ω) ≈ w2 around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully self-consistent and the non-self-consistent ones give different results for the parameters considered here. However, they have similar global results for small densities.

THERMO FIELD DYNAMICS IN TIME REPRESENTATION

1994 ◽  
Vol 09 (07) ◽  
pp. 1153-1180 ◽  
Author(s):  
Y. YAMANAKA ◽  
H. UMEZAWA ◽  
K. NAKAMURA ◽  
T. ARIMITSU
Keyword(s):  
Kinetic Equation ◽  
Time Dependent ◽  
Nonequilibrium Systems ◽  
Renormalization Condition ◽  
Usual Definition ◽  
Time Representation ◽  
Self Energy ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Definition Of

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.

RENORMALIZATION AND BOLTZMANN EQUATIONS IN THERMAL QUANTUM FIELD THEORY

1995 ◽  
Vol 10 (11) ◽  
pp. 1693-1700 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Boltzmann Equation ◽  
Renormalization Scheme ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Boltzmann Equations ◽  
Self Energy ◽  
Spatially Inhomogeneous ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Consistent Manner

The renormalization scheme in nonequilibrium thermal quantum field theories is reexamined. Instead of the self-energy diagonalization scheme, we propose to diagonalize Green’s function at equal time. This eliminates the problem of on-shell definition related to time-dependent energies and spatially inhomogeneous situations, and yields a Boltzmann equation that contains memory effect. The new diagonalization scheme and the derivation of the Boltzmann equation from it can be applied to any thermal situation. It allows the treatment of a nonequilibrium problem beyond perturbational calculations in a self-consistent manner. The results are applicable to both thermo field dynamics and the closed time path formalism.

scholarly journals SPECTRAL PROPERTIES OF THE GENERALISED SPIN-FERMION MODELS

1999 ◽  
Vol 13 (20) ◽  
pp. 2573-2605 ◽  
Author(s):  
A. L. KUZEMSKY
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
General Procedure ◽  
Dyson Equation ◽  
Magnetic Behaviour ◽  
Model Concept ◽  
Excitation Spectra ◽  
Perturbative Approach ◽  
Self Energy ◽  
Many Body Systems

In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the Irreducible Green's Functions (IGF) approach. Examples are generalised d–f model and Kondo–Heisenberg model. The calculations of the quasiparticle excitation spectra with damping for these models has been performed in the framework of the equation-of-motion method for two-time temperature Green's Functions within a non-perturbative approach. A unified scheme for the construction of Generalised Mean Fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation has been generalised in order to include the presence of the two interacting subsystems of localised spins and itinerant electrons. A general procedure is given to obtain the quasiparticle damping in a self-consistent way. This approach gives the complete and compact description of quasiparticles and show the flexibility and richness of the generalised spin-fermion model concept.

Self‐consistent many‐body theory of π‐electron systems. II. Self‐energy effects

1979 ◽  
Vol 70 (9) ◽  
pp. 4086-4090 ◽  
Author(s):  
Marcello Baldo ◽  
Renato Pucci ◽  
Pasquale Tomasello
Keyword(s):  
Electron Systems ◽  
Many Body ◽  
Self Energy ◽  
Many Body Theory ◽  
Self Consistent ◽  
Body Theory

THE SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

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