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Physical review. B, Condensed matter

Anisotropic renormalization-group flow of quasiparticle weight in a two-dimensional electron system with a partially flat Fermi surface

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Jun 15, 1999• 12 citations
Publisher

Abstract

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 $\mathit{k}$ on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.

DOI
10.1103/physrevb.59.14823

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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.
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 implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight ZZZ along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.
We present a renormalization-group analysis of two-dimensional interacting fermion systems with a closed and partially flat Fermi surface. Numerical solutions of the one-loop flow equations show that for a bare local repulsion, the system evolves through three different regimes as the typical energy is lowered: a high-energy transient with a strong competition between particle-particle and particle-hole channels, an intermediate regime with dominant spin-density wave correlations, and finally a ``hot spot'' regime exhibiting d-wave superconductivity. We study, mostly by analytical methods, how this flow pattern depends on the number N of Fermi-surface patches used in the numerical solution. This clearly indicates that the final regime requires vanishingly small microscopic interactions, for the one-loop approximation to be valid, as N is going to infinity.
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.
We consider the application of the two-loop functional renormalization group (fRG) approach to study the low-dimensional Hubbard model. This approach accounts for both the universal and nonuniversal contributions to the RG flow. While the universal contributions were studied previously within the field-theoretical RG for the one-dimensional Hubbard model with linearized electronic dispersion and the two-dimensional Hubbard model with flat Fermi surface, the nonuniversal contributions to the flow of the vertices and susceptibilities appear to be important at large momenta scales. The two-loop fRG approach is also applied to the two-dimensional Hubbard model with a curved Fermi surface and the van Hove singularities near the Fermi level. The vertices and susceptibilities in the end of the flow of the two-loop approach are suppressed in comparison with both the one-loop approach with vertex projection and the modified one-loop approach with corrected vertex projection errors. The results of the two-loop approach are closer to the results of one-loop approach with the projected vertices, the difference of the results of one- and two-loop fRG approaches decreases when going away from the van Hove band filling. The quasiparticle weight remains finite in two dimensions at not too low temperatures above the paramagnetic ground state.