XXZ Model and the Structure of the Symmetric Algebra

MA Zhong-Qi; HOU Bo-Yuan; HOU Bo-Yu

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2024年10月30日

Chinese Physics C> 1991, Vol. 15> Issue(9) : 812-821

XXZ Model and the Structure of the Symmetric Algebra

Institute of High Energy Physics Academia Sinica,Beijing 1000391 Graduate School,Academia Sinica Beijing 1000392 Institute of Modern Physics,Northwest University,Xian 710069

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Abstract：
In this paper,an XXZ model of the Heisenberg spin chain with the symmetry of the quantum SL_q(2) enveloping algebra is discussed.In terms of the structure of the Temperley-Lieb algebra,in this model we analyse the finite-dimensional representations of the quantum SL_q(2) with q^p=±1 in some detail,including the condition of appearance of the reducible but indecomposable representations (type Ⅰ representation),their properties,and the complete set of the states related to a definite energy where the new states are obtained by an appropriare limit process.

References

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Alcaraz F C. Barber M N, Batchelor M T, Baxter R J and Quispel G R W, J. Phys., A20(1987), 6397.[2] Yang C. N. arid Yang C. P. Phys. Rev. 150(1966), 321.[3] H. N. V. Temperley, E. H. Lieb, Proc. Roy. Sac. Lond., A, 322(1971), 25.[4] Drinfel'd V G, Quantum Group, Vol. 1, 798, Proc. 1. C. M. Berkeley 1986.[5] Jimbo M, Lett. Math. Phys., 10(1985), 63.[6] Levy D, Phys. Rev. Lett., 64(1990), 499.[7] Pasquier V and Saleur H, Nucl. Phys., B330(1990), 523.

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MA Zhong-Qi, HOU Bo-Yuan and HOU Bo-Yu. XXZ Model and the Structure of the Symmetric Algebra[J]. Chinese Physics C, 1991, 15(9): 812-821.

MA Zhong-Qi, HOU Bo-Yuan and HOU Bo-Yu. XXZ Model and the Structure of the Symmetric Algebra[J]. Chinese Physics C, 1991, 15(9): 812-821. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

XXZ Model and the Structure of the Symmetric Algebra

Corresponding author: MA Zhong-Qi,

Institute of High Energy Physics Academia Sinica,Beijing 1000391 Graduate School,Academia Sinica Beijing 1000392 Institute of Modern Physics,Northwest University,Xian 710069

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1991-09-05

Abstract: In this paper,an XXZ model of the Heisenberg spin chain with the symmetry of the quantum SL_q(2) enveloping algebra is discussed.In terms of the structure of the Temperley-Lieb algebra,in this model we analyse the finite-dimensional representations of the quantum SL_q(2) with q^p=±1 in some detail,including the condition of appearance of the reducible but indecomposable representations (type Ⅰ representation),their properties,and the complete set of the states related to a definite energy where the new states are obtained by an appropriare limit process.