Magnetic Susceptibility at Zero Temperature for the One-Dimensional Hubbard Model

H. Shiba

doi:10.1103/PhysRevB.6.930

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Magnetic Susceptibility at Zero Temperature for the One-Dimensional Hubbard Model

H. Shiba^*

Department of Physics, University of California, Los Angeles, California 90024

^*Present address: Department of Physics, Faculty of Science, Osaka University, Toyonaka, Japan.

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Phys. Rev. B 6, 930 – Published 1 August, 1972

DOI: https://doi.org/10.1103/PhysRevB.6.930

Abstract

The magnetic susceptibility at absolute-zero temperature for the one-dimensional Hubbard model is studied exactly as a function of the concentration of electrons by using Lieb and Wu's theory for this system. Our analysis essentially follows Griffiths's method for the magnetic susceptibility of the one-dimensional Heisenberg antiferromagnet, and is a generalization of Takahashi's calculation to the systems with an arbitrary concentration of electrons. The ground-state energy and the magnitude of local moments at each site are also studied. Combined with the results on the susceptibility, they should suggest how the effect of the Coulomb interaction on the properties of the system at low temperatures changes with the concentration of electrons.

References (16)

L. H. Lieb and D. C. Mattis, Mathematical Physics in One Dimension (Academic, New York, 1966)
L. H. Lieb and F. Y. Wu, Phys. Rev. Letters 20, 1445 (1968)
H. Bethe, Z. Physik 71, 205 (1931)
L. Hulthen, Ark. Mat. Astron. Fys. 26A, No. 11 (1938)
C. N. Yang, Phys. Rev. Letters 19, 1312 (1967)
A. A. Ovchinnikov, Zh. Eksperim. i Teor. Fiz. 57, 2144 (1970) [Sov. Phys. JETP 30, 1160 (1970)]
M. Takahashi, Progr. Theoret. Phys. (Kyoto) 42, 1098 (1969) ibid.43, 1619 (1970)
H. Shiba and P. A. Pincus, Phys. Rev. B 5, 1966 (1972) H. Shiba, Progr. Theoret. Phys. (Kyoto) (to be published)
L. H. Lieb and D. C. Mattis, Phys. Rev. 125, 164 (1962)
J. Hubbard, Proc. Roy. Soc. (London) A276, 238 (1963) ibid.A281, 401 (1964)
M. C. Gutzwiller, Phys. Rev. Letters 10, 159 (1963)
J. Kanamori, Progr. Theoret. Phys. (Kyoto) 30, 275 (1963)
R. B. Griffiths, Phys. Rev. 133, A768 (1964)
J. Friedel, in Theory of Magnetism in Transition Metals, edited by W. Marshall (Academic, New York, 1967), p. 283
C. N. Yang and C. P. Yang, Phys. Rev. 151, 258 (1966)
D. R. Penn, Phys. Rev. 142, 350 (1966)

[c1] L. H. Lieb and D. C. Mattis, Mathematical Physics in One Dimension (Academic, New York, 1966)

[c2] L. H. Lieb and F. Y. Wu, Phys. Rev. Letters 20, 1445 (1968)

[c3] H. Bethe, Z. Physik 71, 205 (1931)

[c4] L. Hulthen, Ark. Mat. Astron. Fys. 26A, No. 11 (1938)

[c5] C. N. Yang, Phys. Rev. Letters 19, 1312 (1967)

[c6] A. A. Ovchinnikov, Zh. Eksperim. i Teor. Fiz. 57, 2144 (1970) [Sov. Phys. JETP 30, 1160 (1970)]

[c7] M. Takahashi, Progr. Theoret. Phys. (Kyoto) 42, 1098 (1969) ibid.43, 1619 (1970)

[c8] H. Shiba and P. A. Pincus, Phys. Rev. B 5, 1966 (1972) H. Shiba, Progr. Theoret. Phys. (Kyoto) (to be published)

[c9] L. H. Lieb and D. C. Mattis, Phys. Rev. 125, 164 (1962)

[c10] J. Hubbard, Proc. Roy. Soc. (London) A276, 238 (1963) ibid.A281, 401 (1964)

[c11] M. C. Gutzwiller, Phys. Rev. Letters 10, 159 (1963)

[c12] J. Kanamori, Progr. Theoret. Phys. (Kyoto) 30, 275 (1963)

[c13] R. B. Griffiths, Phys. Rev. 133, A768 (1964)

[c14] J. Friedel, in Theory of Magnetism in Transition Metals, edited by W. Marshall (Academic, New York, 1967), p. 283

[c15] C. N. Yang and C. P. Yang, Phys. Rev. 151, 258 (1966)

[c16] D. R. Penn, Phys. Rev. 142, 350 (1966)

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Magnetic Susceptibility at Zero Temperature for the One-Dimensional Hubbard Model

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