scholarly journals Erratum: Functional-derivative study of the Hubbard model. II. Self-consistent equation and its complete solution

1980 ◽  
Vol 22 (2) ◽  
pp. 1123-1123
Author(s):  
Tadashi Arai ◽  
Morrel H. Cohen
Keyword(s):  
Hubbard Model ◽  
Complete Solution ◽  
Functional Derivative ◽  
Self Consistent ◽  
Consistent Equation

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.

scholarly journals Antiferromagnetism in the Hubbard model on the honeycomb lattice: A two-particle self-consistent study

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
S. Arya ◽  
P. V. Sriluckshmy ◽  
S. R. Hassan ◽  
A.-M. S. Tremblay
Keyword(s):  
Hubbard Model ◽  
Honeycomb Lattice ◽  
Self Consistent

A Parallel Algorithm for Conserving Approximation of Lattice Models Having Both Interactions and Disorder

2001 ◽  
Vol 15 (24n25) ◽  
pp. 3270-3278
Author(s):  
B. Buhrow ◽  
J. J. Deisz
Keyword(s):  
Perturbation Theory ◽  
Hubbard Model ◽  
Specific Heat ◽  
Parallel Algorithm ◽  
Lattice Models ◽  
Numerical Calculations ◽  
Self Consistent ◽  
Attractive Hubbard Model ◽  
Local Pairing ◽  
Diagonal Disorder

We present a parallel algorithm for numerical calculations for electronic lattice models with interactions and disorder. In this scheme, diagonal and off-diagonal disorder are treated exactly per disorder configuration and interaction effects are evaluated using conserving approximations based on self-consistent perturbation theory. We demonstrate this method by calculating second-order corrections to the local pairing amplitude and specific heat for the attractive Hubbard model.

THE SELF CONSISTENT COHERENT POTENTIAL APPROXIMATION TO THE HUBBARD MODEL

1990 ◽  
Vol 04 (08) ◽  
pp. 549-560 ◽  
Author(s):  
MASSIMO CORRIAS
Keyword(s):  
Hubbard Model ◽  
Interaction Strength ◽  
Exact Formula ◽  
Coherent Potential Approximation ◽  
The Self ◽  
Potential Approximation ◽  
Double Occupancy ◽  
Occupancy Probability ◽  
Self Consistent

We introduce, by an exact formula for the double occupancy probability δ in the Hubbard model, a self consistent version of the CPA which is aimed at taking into better account correlations of the electrons motion. We show that CPA breaks down at large values of the interaction strength, and we suggest a way of overcoming this limitation along the lines of the model proposed here.

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