scholarly journals Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model

2016 ◽  
Vol 93 (19) ◽  
Author(s):  
P. Pudleiner ◽  
T. Schäfer ◽  
D. Rost ◽  
G. Li ◽  
K. Held ◽  
...  
Keyword(s):  
Hubbard Model ◽  
The Self ◽  
Two Dimensional ◽  
Self Energy

ANISOTROPIC PSEUDOGAP IN THE HALF-FILLING TWO-DIMENSIONAL HUBBARD MODEL AT FINITE TEMPERATURE

2000 ◽  
Vol 14 (21) ◽  
pp. 2271-2286
Author(s):  
TAIICHIRO SAIKAWA ◽  
ALVARO FERRAZ
Keyword(s):  
Fermi Surface ◽  
Fermi Level ◽  
Hubbard Model ◽  
Spectral Function ◽  
Density Of States ◽  
Spin Fluctuation ◽  
The Self ◽  
Two Dimensional ◽  
Self Energy ◽  
Half Filling

We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.

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.

Second order self-energy of the two-dimensional Hubbard model

1997 ◽  
Vol 103 (1) ◽  
pp. 41-44 ◽  
Author(s):  
Stéphane Daul ◽  
Michael Dzierzawa
Keyword(s):  
Hubbard Model ◽  
Second Order ◽  
Two Dimensional ◽  
Self Energy

SINGULAR FERMI SURFACES II: THE TWO-DIMENSIONAL CASE

2008 ◽  
Vol 20 (03) ◽  
pp. 275-334 ◽  
Author(s):  
JOEL FELDMAN ◽  
MANFRED SALMHOFER
Keyword(s):  
Perturbation Theory ◽  
Spatial Dimension ◽  
Physical Significance ◽  
The Self ◽  
Two Dimensional ◽  
Singular Case ◽  
Fermi Surfaces ◽  
Self Energy ◽  
Fermion Systems ◽  
Derivatives Of

We consider many-fermion systems with singular Fermi surfaces, which contain Van Hove points where the gradient of the band function k ↦ e(k) vanishes. In a previous paper, we have treated the case of spatial dimension d ≥ 3. In this paper, we focus on the more singular case d = 2 and establish properties of the fermionic self-energy to all orders in perturbation theory. We show that there is an asymmetry between the spatial and frequency derivatives of the self-energy. The derivative with respect to the Matsubara frequency diverges at the Van Hove points, but, surprisingly, the self-energy is C1 in the spatial momentum to all orders in perturbation theory, provided the Fermi surface is curved away from the Van Hove points. In a prototypical example, the second spatial derivative behaves similarly to the first frequency derivative. We discuss the physical significance of these findings.

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