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Theoretical and Mathematical Physics

A method of self-consistent perturbation theory with respect to the energy overlap integral in the Hubbard model

E. G. Goryachev, Evgeniy V. Kuz’min

Published Dec 1, 1990• 1 citation
Publisher
DOI
10.1007/bf01018407

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I present a numerical treatment for a certain class of Feynman diagrams in perturbation theory with respect to the Coulomb correlation U. This method is formally exact for the frequency integrals occurring in the expression for the retarded Green's function. I specify this method to the self-consistent second-order perturbation theory (SOPT) for the single-impurity Anderson model and to the self-consistent fluctuation exchange approximation (FLEX) for the Hubbard model in infinite dimensions d\ensuremath{\rightarrow}\ensuremath{\infty}. The presented treatment is not only restricted to the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. I present the resulting equations for the retarded self-energy, numerical results for the self-energy, density of states and the interaction spectrum in the FLEX for different scalings of the real frequency axis. The numerical solution of the SOPT and the FLEX could be obtained with very little numerical effort. In this form the calculation is nearly independent of the temperature and over a wide range nearly independent of the value of U. The computational time and the memory requirement for the solution of the self-energy equation are reduced to a minimum in this numerical treatment. \textcopyright{} 1996 The American Physical Society.
I present a numerical treatment for the retarded self-energy in two dimensions (2D), which is formally exact for the frequency and the momentum sums occurring in perturbation theory with respect to the Coulomb interaction U. In this frequency- and momentum-renormalization-group technique, which allows the sequential elimination of regions of high frequencies and momenta, I focus on the 2D fluctuation-exchange approximation for the Hubbard model. I present results for the self-energy and the spectral density down to temperatures t=${10}^{\mathrm{\ensuremath{-}}4}$/t (the next neighbor hopping amplitude). The obtained result shows evidence for a Fermi-liquid phase for bandfillings n near half filling for U/t=2 to U/t=8 for T\ensuremath{\rightarrow}0.