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Prog. Theor. Phys. Vol. 78 No. 5 (1987) pp. 1009-1021
Completeness of the Two-Down-Spin Bethe States in the One-Dimensional Heisenberg Model
Tohru Koma and
Hiroshi Ezawa
Department of Physics, Gakushuin University, Tokyo 171
(Received April 30, 1987)
Abstract:
For the one-dimensional spin-1/2 XXZ-Heisenberg model, it is shown that the system of two-down-spin energy eigenstates as obtained by the Bethe ansatz is complete in the two-down-spin subspace when the system is constructed with due caution. The completeness has so far been left obscure due to that singular nature of the construction process of the states, which we circumvent by first modifying the periodic boundary condition of the model and then applying a limiting process to the modified eigenstates to restore the condition.
URL :
http://ptp.ipap.jp/link?PTP/78/1009/
DOI : 10.1143/PTP.78.1009
References:
- H. A. Bethe, Z. Phys. 71 (1931), 205.
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C. N. Yang and C. P. Yang, Phys. Rev. 150 (1966), 321[APS].
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M. Takahashi and M. Yamada, J. Phys. Soc. Jpn. 54 (1985), 2808[JPSJ].
- Y. Kato, N. Mugibayashi and K. Sekine, RIMS Kôkyûroku No. 159, 1972 (The Hamiltonian, its definition and spectrum), p. 69, Research Institute for Mathematical Sciences, Kyoto University, Kyoto [in Japanese].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1213-1218
:
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Thermal Bethe-Ansatz Method for the One-Dimensional Heisenberg Model
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Tohru Koma
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Progress of Theoretical Physics Vol. 81 No. 4 (1989) pp. 783-809
:
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Thermal Bethe-Ansatz Method for the Spin-1/2 XXZ Heisenberg Chain
-
Tohru Koma
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Progress of Theoretical Physics Vol. 83 No. 4 (1990) pp. 655-659
:
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An Extension of the Thermal Bethe Ansatz
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Tohru Koma
