### 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 language | English |
---|---|

Pages (from-to) | 529-545 |

Number of pages | 17 |

Journal | Journal of Low Temperature Physics |

Volume | 12 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Sep 1973 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Low Temperature Physics*,

*12*(5-6), 529-545. https://doi.org/10.1007/BF00654955

**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.** / Menyhard, N.; Sólyom, J.

Research output: Contribution to journal › Article

*Journal of Low Temperature Physics*, vol. 12, no. 5-6, pp. 529-545. https://doi.org/10.1007/BF00654955

}

TY - JOUR

T1 - 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

AU - Menyhard, N.

AU - Sólyom, J.

PY - 1973/9

Y1 - 1973/9

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0000410231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000410231&partnerID=8YFLogxK

U2 - 10.1007/BF00654955

DO - 10.1007/BF00654955

M3 - Article

AN - SCOPUS:0000410231

VL - 12

SP - 529

EP - 545

JO - Journal of Low Temperature Physics

JF - Journal of Low Temperature Physics

SN - 0022-2291

IS - 5-6

ER -