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

Abstract
HTML
Reference
Related

PDF

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

[1]

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.

[1]	QIN Meng,LI Yan-Biao,BAI Zhong,LIN Shang-Jin,LIU Wei. Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriyacouplings and an inhomogeneous magnetic field. Chinese Physics C, 2010, 34(11): 1693-1695.doi:10.1088/1674-1137/34/11/004
[2]	QIN Meng,TIAN Dong-Ping. Bipartite entanglement in a two-qubit Heisenberg XXZ chain under aninhomogeneous magnetic field. Chinese Physics C, 2009, 33(4): 249-251.doi:10.1088/1674-1137/33/4/002
[3]	QIN Meng,TAO Ying-Juan,TIAN Dong-Ping. Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain. Chinese Physics C, 2008, 32(9): 710-713.doi:10.1088/1674-1137/32/9/007
[4]	LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map. Chinese Physics C, 2002, 26(4): 402-408.
[5]	LIU Yu-Xin. Algebraic Model Description of High Spin Superdeformed Bands. Chinese Physics C, 2000, 24(S1): 50-53.
[6]	Ni Zhixiang. Nonlinear Spectrum-Generating Algebra for the Symmetrical Pöschl-Teller Potential. Chinese Physics C, 1999, 23(3): 289-297.
[7]	Xi Xiaoqiang,Shi Kangjie,Hou Boyu,Fan Heng. Algebraic Bethe Ansatz for the Supersymmetric t-J Model With Reflecting Boundary Conditions in FBF Background. Chinese Physics C, 1999, 23(10): 961-979.
[8]	Wang Zhengda,Zhang Xiaodong,Wang Xiaochun,Wang Xiaobin. Self-Similar Strcture Shell Model. Chinese Physics C, 1998, 22(4): 333-340.
[9]	Yu Zhaoxian,Zhang Dexing,Liu Yehou. Algebraic Structure of Two-Parameter Deformed Multi-mode Bose Operators and Their Applications (Ⅱ). Chinese Physics C, 1998, 22(1): 28-33.
[10]	Yu Zhaoxian,Zhang Dexing,Liu Yehou. Algebraic Structure of Two-Parameter Deformed Multi-mode Bose Operators and Their Applications (Ⅲ). Chinese Physics C, 1998, 22(3): 225-233.
[11]	Shi Kangjie,Yang Wenli,Fan Heng,Hou Boyu. Bosonized Vertex Operators Realize Z-F Algebra for Z_nSymmetric Belavin R Matrix. Chinese Physics C, 1997, 21(8): 706-713.
[12]	Yu Zhaoxian,Zhang Dexing,Liu Yehou. Algbraic Structure of Two-Parameter Deformed Multi-Mode Bose Operators and Their Applications (Ⅰ). Chinese Physics C, 1997, 21(11): 999-1004.
[13]	Shi Kangjie,Yang Wenli,Hou Boyu,Fan Heng. q-deformed Quantum Affine Algebra in Z_nLattice Model. Chinese Physics C, 1995, 19(3): 229-240.
[14]	HOU Bo-Yu,ZHAO Liu. Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅰ) General Framework. Chinese Physics C, 1993, 17(1): 28-37.
[15]	HOU Bo-Yu,ZHAO Liu. On the Connections of W Algebras from Different Reductions of WZNW Theory. Chinese Physics C, 1993, 17(4): 329-337.
[16]	HAO San-Ru. The Hidden Symmetries and Their Algebraic Structure of the Static Axially Symmetric SDYM Fields. Chinese Physics C, 1993, 17(6): 538-543.
[17]	ZHAO Liu. On the Exchange Algebra of Periodic WZNW model. Chinese Physics C, 1992, 16(7): 609-614.
[18]	XU Kai-Wen,SHEN Jian-Min. THE VIRASORO ALGEBRA ON TORUS WITH GENERAL METRIC. Chinese Physics C, 1989, 13(7): 594-599.
[19]	ZENG Xin-Chuan,HU Shi-Ke. THE STUDY OF BARYON STRUCTURE IN THE SKYRME MODEL. Chinese Physics C, 1987, 11(4): 469-475.
[20]	WU Yong-Shi,GE Mo-Lin. NONLOCAL INFINITELY CONSERVED CURRENTS AND KAC-MOODY ALGEBRAIC STRUCTURE OF O(N) SUPER-CHIRAL MODEL. Chinese Physics C, 1983, 7(4): 427-436.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(3277)
PDF Downloads(462)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者:陈斌, bchen63@163.com

1.
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.