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arXiv:cond-mat/9911115 · Recent Progress in Many-Body Theories

TWO-LOOP RENORMALIZATION OF THE QUASIPARTICLE WEIGHT IN TWO-DIMENSIONAL ELECTRON SYSTEMS

JUN-ICHIRO KISHINE, Nobuo Furukawa, KENJI YONEMITSU

Published Sep 1, 2000• 0 citations
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Abstract

We apply the renormalization-group (RG) approach to two model systems where the two-dimensional Fermi surface has portions which give rise to the logarithmically singular two-loop self-energy process.
DOI
10.1142/9789812792754_0013

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Two-loop renormalization-group (RG) analysis for a two-dimensional electron system with a partially flat Fermi surface has been carried out. We found that the RG flow of the quasiparticle weight depends on the location of the electron wave number k\mathit{k}k on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.
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Two-loop renormalization-group analysis for a two-dimensional electron system with a partially flat Fermi surface has been carried out. We found that, {\it irrespective of pairing mechanism}, the quasiparticle weight is anisotropically suppressed due to logarithmically singular processes in the flat regions of the Fermi surface. When the energy scale decreases, the quasiparticle weight is the most strongly suppressed around the center of the flat region, which qualitatively agrees with the anisotropic pseudogap behavior suggested through the angle-resolved photoemission spectroscopy experiments for underdoped Bi2_22​Sr2_22​CaCu2_22​O8_88​.
We present the formalism for a two-loop renormalization group (RG) calculation of some order-parameter susceptibilities associated with a two-dimensional (2D) flat Fermi-surface model. In this order of perturbation theory, one must take into account the self-energy effects directly in all RG flow equations. In one-loop order, our calculation reproduces the well-known results obtained previously by other RG schemes. That is, for repulsive interactions all susceptibilities diverge in the low-energy limit and the antiferromagnetic (AF) spin-density-wave correlations produce indeed the leading instability in the system. In contrast, in two-loop order, only the AF susceptibility diverges for this model. However, even this divergence takes place at a much slower rate than in the one-loop RG approach. The purpose of this paper is to show in a very simple setting how to assess the importance of two-loop quantum fluctuations in 2D interacting fermionic models. With some modifications, the present formalism can also be extended to discuss more realistic models such as the paradigmatic 2D Hubbard model.
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