Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky-Moriya interaction

doi:10.1088/1674-1056/24/10/107502

Abstract

We propose an integrable spin-1/2Heisenberg model where the exchange couplings and Dzyloshinky-Moriya interactions are dependent on the sites. By employing the quantum inverse scattering method, we obtain the eigenvalues and the Bethe ansatz equation of the system with the periodic boundary condition. Furthermore, we obtain the exact solution and study the boundary effect of the system with the anti-periodic boundary condition via the off-diagonal Bethe ansatz. The operator identities of the transfer matrix at the inhomogeneous points are proved at the operator level. We construct the T-Q relation based on them. From which, we obtain the energy spectrum of the system. The corresponding eigenstates are also constructed. We find an interesting coherence state that is induced by the topological boundary.

Keywords: Bethe ansatz Yang-Baxter equation T-Q relation

Received: 08 June 2015
Revised: 08 July 2015
Accepted manuscript online:

PACS:	75.10.Pq	(Spin chain models)
	03.65.Vf	(Phases: geometric; dynamic or topological)
	71.10.Pm	(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11174335, 11375141, 11374334, and 11434013) and the National Program for Basic Research of China and the Fund from the Chinese Academy of Sciences.

Corresponding Authors: Yang Li-Jun
E-mail: chortley@iphy.ac.cn

Cite this article:

Yang Li-Jun (杨丽君), Cao Jun-Peng (曹俊鹏), Yang Wen-Li (杨文力) Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky-Moriya interaction 2015 Chin. Phys. B 24 107502

[1]	Yang C N 1968 Phys. Rev. 168 1920
[2]	Yang C N 1967 Phys. Rev. Lett. 19 1312
[3]	Baxter R J 1971 Phys. Rev. Lett. 26 832
[4]	Baxter R J 1971 Phys. Rev. Lett. 26 834
[5]	Sklyanin E K and Faddeev L D 1978 Sov. Phys. Dokl. 23 902
[6]	Takhtadzhan L A and Faddeev L D 1979 Rush. Math. Surveys. 34 11
[7]	Sklyanin E K, Takhtajan L A and Faddeev L D 1980 Theor. Math. Phys. 40 688
[8]	Faddeev L D 1980 Sov. Sci. Rev. Math. C 1 107
[9]	Sklyanin E K 1982 J. Sov. Math. 19 1546
[10]	Cherednik I 1984 Theor. Math. Phys. 61 977
[11]	Alcaraz F C, Barber M N, Batchelor M T, Baxter R J and Quispel G R W 1987 J. Phys. A: Math. Gen. 20 6397
[12]	Sklyanin E K 1988 J. Phys. A: Math. Gen. 21 2375
[13]	Kulish P P and Reshetikhin N 1981 JHTP 53 108
[14]	De Vega H J and Lopes E 1911 Phys. Rev. Lett. 67 489
[15]	Lopes E 1992 Nucl. Phys. B 370 636
[16]	Sutherland B 1975 Phys. Rev. B 12 3795
[17]	Cao J P, Yang W L, Shi K J and Wang Y P 2013 Phys. Rev. Lett. 111 137201
[18]	Cao J P, Yang W L, Shi K J and Wang Y P 2013 Nucl. Phys. B 877 152
[19]	Li Y Y, Cao J P, Yang W L, Shi K J and Wang Y P 2014 Nucl. Phys. B 884 17
[20]	Cao J P, Yang W L, Shi K J and Wang Y P 2014 Nucl. Phys. B 886 185
[21]	Cao J P, Yang W L, Shi K J and Wang Y P 2014 J. High Energy Phys. 04 143
[22]	Nepomechie R I 2013 J. Phys. A: Math. Theor. 46 442002
[23]	Dzyaloshinsky I E 1958 J. Phys. Chem. Solids 4 241
[24]	Moriya T 1960 Phys. Rev. Lett. 4 228
[25]	Moriya T 1960 Phys. Rev. 120 91
[26]	Yi L, Büttner G, Usadel D and Yao K L 1993 Phys. Rev. B 47 254
[27]	Koshibae W, Ohta Y and Maekawa S 1993 Phys. Rev. Lett. 71 467
[28]	de Sousa J R, de Albuquerque D F and Fittipaldi I P 1994 Phys. Lett. A 191 275
[29]	Daniel M and Amuda R 1996 Phys. Rev. B 53 R2930
[30]	Zhang D G, Cheng L and Li B Z 1999 Phys. Rev. B 59 8379

[1]	Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields Jia-Sheng Dong(董家生), Pengcheng Lu(路鹏程), Pei Sun(孙佩), Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), Kun Hao(郝昆), and Wen-Li Yang(杨文力). Chin. Phys. B, 2023, 32(1): 017501.
[2]	Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Chin. Phys. B, 2021, 30(5): 050201.
[3]	Exact solution of an integrable quantum spin chain with competing interactions Jian Wang(王健), Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), and Wen-Li Yang(杨文力). Chin. Phys. B, 2021, 30(11): 117501.
[4]	Exact solution of a topological spin ring with an impurity Xu-Chu Huang(黄旭初), Yi-Hua Song(宋艺华), Yi Sun(孙毅). Chin. Phys. B, 2020, 29(6): 067501.
[5]	Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method M Baradaran, H Panahi. Chin. Phys. B, 2017, 26(6): 060301.
[6]	A 9×9 matrix representation of Temperley–Lieb algebra and corresponding entanglement Gou Li-Dan(苟立丹) and Zhu Rui-Han(朱瑞晗) . Chin. Phys. B, 2012, 21(2): 020305.
[7]	BETHE ANSATZ FOR SUPERSYMMETRIC MODEL WITH U_q[osp(1\|2)] SYMMETRY Yang Wen-li (杨文力). Chin. Phys. B, 2001, 10(2): 109-112.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky-Moriya interaction

Cite this article:

Online attention