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arXiv:cond-mat/9411026

Improved Treatment of Frequency Sums in Propagator-Renormalized Perturbation Theories

J. J. Deisz, D. W. Hess, Joseph W. Serene

Published Nov 4, 1994• 0 citations
arXivHTMLPDF

Abstract

We present a massively parallel algorithm for calculating the self-energy in self-consistent finite temperature perturbation theory for lattice models. The algorithm uses analytic functions with appropriate asymptotic high frequency behavior and fast Fourier transforms to accurately calculate the self-energy at low-frequency. Traditional methods that truncate the high frequency tails of the temperature Green's function lead to `contamination' of the low-frequency behavior of the self-energy. Our algorithm is both accurate and scalable. We compare results for the Hubbard model using various techniques for handling the high frequency tails of the temperature Green's function.

DOI
10.48550/arxiv.cond-mat/9411026

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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.
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