Application of the renormalization group technique to the problem of phase transition in one-dimensional metallic systems. I. Invariant couplings, vertex, and one-particle Green's function

N. Menyhard, J. Sólyom

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Abstract

A one-dimensional system of electrons interacting via a BCS-type interaction is investigated by renormalization group techniques in two successive approximations at T=0, keeping only a single energy variable ω. The first approximation is equivalent to the summation of leading logarithmic terms carried out by Bychkov et al., and correspondingly the vertex function displays a singularity at a finite value of ω. The second approximation accounts for the next leading logarithmic terms as well, and by this means the singularity is shown to be pushed down to ω=0. Due to important self-energy contributions, however, the invariant couplings behave differently and tend to a saturation value at ω=0.

Original languageEnglish
Pages (from-to)529-545
Number of pages17
JournalJournal of Low Temperature Physics
Volume12
Issue number5-6
DOIs
Publication statusPublished - Sep 1973

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Green's function
apexes
Green's functions
Phase transitions
Electrons
approximation
saturation
energy
electrons
interactions

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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AB - A one-dimensional system of electrons interacting via a BCS-type interaction is investigated by renormalization group techniques in two successive approximations at T=0, keeping only a single energy variable ω. The first approximation is equivalent to the summation of leading logarithmic terms carried out by Bychkov et al., and correspondingly the vertex function displays a singularity at a finite value of ω. The second approximation accounts for the next leading logarithmic terms as well, and by this means the singularity is shown to be pushed down to ω=0. Due to important self-energy contributions, however, the invariant couplings behave differently and tend to a saturation value at ω=0.

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