### Abstract

The two dimensional Hubbard model with repulsive interaction is studied in the tz.sbnd;matrixapproximation. At T = 0 the particle-particle correlation function and the tz.sbnd;matrix are obtained analytically so that it is shown that the tz.sbnd;matrix and hence the self-energy have no singularities in the upper half phase of the complex energy variable. The phase angle of the tz.sbnd;matrix δ(2k_{F}+q,ω), in the limit q→0 and ω→0, is found to depend on the ratio ω/q and is not always zero. This non-vanishing phase angle results in the logarithmic correction to the imaginary part of the self-energy as ImΣ(k_{F},ε{lunate}) ∝ ε{lunate}^{2} lm |ε{lunate}|. However, the renormalization factor Z is finite at the Fermi surface suggesting that the stability of the Fermi liquid state at least within the conventional perturbation theory. The case of the attractive interaction has also been studied and the crossover from the Cooper pairing to the real-space pairing is indicated.

Original language | English |
---|---|

Pages (from-to) | 1537-1538 |

Number of pages | 2 |

Journal | Physica C: Superconductivity and its applications |

Volume | 185-189 |

Issue number | PART 3 |

DOIs | |

Publication status | Published - Dec 1 1991 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Energy Engineering and Power Technology
- Electrical and Electronic Engineering

### Cite this

*Physica C: Superconductivity and its applications*,

*185-189*(PART 3), 1537-1538. https://doi.org/10.1016/0921-4534(91)90895-6

**Two-dimensional Hubbard model in low electron density limit.** / Narikiyo, Osamu; Hasegawa, Yasumasa; Fukuyama, Hidetoshi.

Research output: Contribution to journal › Article

*Physica C: Superconductivity and its applications*, vol. 185-189, no. PART 3, pp. 1537-1538. https://doi.org/10.1016/0921-4534(91)90895-6

}

TY - JOUR

T1 - Two-dimensional Hubbard model in low electron density limit

AU - Narikiyo, Osamu

AU - Hasegawa, Yasumasa

AU - Fukuyama, Hidetoshi

PY - 1991/12/1

Y1 - 1991/12/1

N2 - The two dimensional Hubbard model with repulsive interaction is studied in the tz.sbnd;matrixapproximation. At T = 0 the particle-particle correlation function and the tz.sbnd;matrix are obtained analytically so that it is shown that the tz.sbnd;matrix and hence the self-energy have no singularities in the upper half phase of the complex energy variable. The phase angle of the tz.sbnd;matrix δ(2kF+q,ω), in the limit q→0 and ω→0, is found to depend on the ratio ω/q and is not always zero. This non-vanishing phase angle results in the logarithmic correction to the imaginary part of the self-energy as ImΣ(kF,ε{lunate}) ∝ ε{lunate}2 lm |ε{lunate}|. However, the renormalization factor Z is finite at the Fermi surface suggesting that the stability of the Fermi liquid state at least within the conventional perturbation theory. The case of the attractive interaction has also been studied and the crossover from the Cooper pairing to the real-space pairing is indicated.

AB - The two dimensional Hubbard model with repulsive interaction is studied in the tz.sbnd;matrixapproximation. At T = 0 the particle-particle correlation function and the tz.sbnd;matrix are obtained analytically so that it is shown that the tz.sbnd;matrix and hence the self-energy have no singularities in the upper half phase of the complex energy variable. The phase angle of the tz.sbnd;matrix δ(2kF+q,ω), in the limit q→0 and ω→0, is found to depend on the ratio ω/q and is not always zero. This non-vanishing phase angle results in the logarithmic correction to the imaginary part of the self-energy as ImΣ(kF,ε{lunate}) ∝ ε{lunate}2 lm |ε{lunate}|. However, the renormalization factor Z is finite at the Fermi surface suggesting that the stability of the Fermi liquid state at least within the conventional perturbation theory. The case of the attractive interaction has also been studied and the crossover from the Cooper pairing to the real-space pairing is indicated.

UR - http://www.scopus.com/inward/record.url?scp=0026369022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026369022&partnerID=8YFLogxK

U2 - 10.1016/0921-4534(91)90895-6

DO - 10.1016/0921-4534(91)90895-6

M3 - Article

AN - SCOPUS:0026369022

VL - 185-189

SP - 1537

EP - 1538

JO - Physica C: Superconductivity and its Applications

JF - Physica C: Superconductivity and its Applications

SN - 0921-4534

IS - PART 3

ER -