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arXiv:2201.04823

Interaction flow method reloaded

Rohe, Daniel

Published Jan 13, 2022• 0 citations
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Abstract

A recently proposed extension of the interaction flow method is applied to exemplary cases of selected physical and methodical parameters for the two-dimensional Hubbard model away from half-filling and perfect nesting. In this scheme, the self-energy is calculated on the real-frequency axis and its feedback on the flow of interactions is included in a simple manner via a momentum-dependent quasi-particle weight. Results for two different types of self-energy feedback are compared to the case without feedback and to existing results stemming from calculations for imaginary frequencies. Various physical and non-physical aspects which influence the outcome qualitatively and quantitatively are addressed. Some tentative directions for future developments are suggested.

DOI
10.48550/arxiv.2201.04823

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The density of states (DOS) of the two-dimensional Hubbard model is calculated in second-order perturbation with respect to the on-site Coulomb interaction U . The direct analytic continuation formula is presented to calculate the self-energy on the real-frequency axis. The momentum as well as the energy integral in the self-energy is seriously carried out with use of the Fast-Fourier-Transformation algorithm. Near the half-filling, the imaginary part of the self-energy becomes proportional to the energy in the vicinity of the Fermi level in our weak-coupling calculation. In the interacting case, the van Hove singularity (VHS) in DOS is smeared by the self-energy effect, but there still exists a sharp peak structure due to VHS.
The authors have calculated the electronic self-energy of the two-dimensional Hubbard model as a function of frequency and momentum for various band fillings. They present this up to second order in the interaction parameter and also up to infinite order for ladder diagrams in the two-particle scattering channel. The authors have carried out direct k-space integrations using a triangle method. For a half-filled perfectly nested band, the imaginary part, lm Sigma (k f , omega ), has a linear- omega dependence for nested Fermi surfaces which is consistent with the marginal Fermi liquid phenomenology for high-T c superconductors. At, and near, half-filling there is a strong low-energy peak in lm Sigma (2) (k, omega ) when k is off the Fermi surface. The physical origin of this peak is discussed. The peak is enhanced in the ladder approximation. The corresponding structure in Re Sigma (2) (k, omega ) leads to multiple solutions of the Dyson equation for a wide range of values of the parameters. This leads to an appealing explanation of observed structure in some experimental angle-resolved photoemission spectra of high-T c materials. The authors also find anti-bound states split off from the band in the two-particle scattering ladders consistent with the suggestion of Anderson.
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