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Prog. Theor. Phys. Vol. 42 No. 5 (1969) pp. 1098-1105

[ Full Text PDF : FREE ACCESS (322K) ]

Magnetization Curve for the Half-Filled Hubbard Model

Minoru Takahashi

Department of Physics, University of Tokyo, Tokyo

(Received June 3, 1969)

Abstract:

The lowest energies of the one-dimensional half-filled Hubbard model as a function of the total spin are computed from the exact solution of one-dimensional interacting fermions. The lowest energies are used to calculate the magnetization curve at zero temperature. In the case of repulsive interaction our work is an extension of Griffith's theory for the Heisenberg model to the itinerant electron model of antiferromagnet. In the case of attractive interaction it is shown that the magnetic susceptibility in zero field vanishes.


URL : http://ptp.ipap.jp/link?PTP/42/1098/
DOI : 10.1143/PTP.42.1098

[ Full Text PDF : FREE ACCESS (322K) ] Citation:

See Also:

References:

  1. R. B. Griffiths, Phys. Rev. 133 (1964), A 768[APS].
  2. J. Hubbard, Proc. Roy. Soc. A 276 (1963), 238; ibid. 277 (1964), 237.
  3. E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20 (1968), 1445[APS].
  4. C. N. Yang and C. P. Yang, Phys. Rev. 150 (1966), 327[APS].
  5. M. Gaudin, Phys. Lett. A 24 (1967), 55[CrossRef]; thesis, University of Paris, 1967 (unpublished).
  6. M. Takahashi, thesis, University of Tokyo, 1969 (unpublished).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 3582-3592 :
    Variational Monte-Carlo Studies of Hubbard Model. II
    Hisatoshi Yokoyama and Hiroyuki Shiba
  2. Journal of the Physical Society of Japan 59 (1990) pp. 1357-1365 :
    Thermodynamic Quantities of the One-Dimensional Hubbard Model at Finite Temperatures
    Tatsuya Usuki, Norio Kawakami and Ayao Okiji
  3. Journal of the Physical Society of Japan 63 (1994) pp. 401-404 :
    Magnetization Curve of the Infinite-Dimensional Hubbard Model
    Tetsuro Saso and Takumi Hayashi
  4. Journal of the Physical Society of Japan 64 (1995) pp. 4331-4344 :
    Logarithmic Correction Terms of the Magnetic Susceptibility in Highly Correlated Electron Systems
    Kenro Kawano and Minoru Takahashi
  5. Journal of the Physical Society of Japan 64 (1995) pp. 4392-4401 :
    Crossover of Spin Correlations in One-Dimensional Hubbard Model Studied by Quantum Monte Carlo Method
    Youichirou Iino and Masatoshi Imada
  6. Journal of the Physical Society of Japan 76 (2007) 034716 (8 pages) :
    Variational Monte Carlo Analysis of Hubbard Model with Confining Potential: One-dimensional Fermionic Optical Lattice Systems
    Yusuke Fujihara, Akihisa Koga, and Norio Kawakami
  7. Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1076-1085 :
    Singularity of Nonlinear Response near the Critical Field. I
    Masuo Suzuki
  8. Progress of Theoretical Physics Vol. 43 No. 6 (1970) pp. 1619-1619 :
    Magnetic Susceptibility for the Half-Filled Hubbard Model
    Minoru Takahashi
  9. Progress of Theoretical Physics Vol. 44 No. 2 (1970) pp. 348-358 :
    Ground State Energy of the One-Dimensional Electron System with Short-Range Interaction. I
    Minoru Takahashi
  10. Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 69-82 :
    One-Dimensional Hubbard Model at Finite Temperature
    Minoru Takahashi
  11. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 103-114 :
    Low-Temperature Specific-Heat of One-Dimensional Hubbard Model
    Minoru Takahashi
  12. Progress of Theoretical Physics Vol. 53 No. 4 (1975) pp. 955-969 :
    Possible Phases and Some Properties of the One-Dimensional Metal with the Half-Filled Band
    Minoru Kimura
  13. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 758-769 :
    Magnetic Susceptibility of the Strongly Correlated Hubbard Model
    Kenn Kubo
  14. Progress of Theoretical Physics Supplement No.101 (1990) pp. 429-440 :
    Characteristics of Dressed Particles in the 1D Correlated Electron Systems
    Norio Kawakami and Ayao Okiji
  15. Progress of Theoretical Physics Supplement No.108 (1992) pp. 251-263 :
    Exact Solution of Correlated Electron Systems
    Norio Kawakami and Ayao Okiji

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