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Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions |
| Fa-Kai Wen(温发楷)1,† and Xin Zhang(张鑫)2 |
1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2 Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany |
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Abstract We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore, it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.
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Received: 31 August 2020
Revised: 24 October 2020
Accepted manuscript online: 01 December 2020
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PACS:
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02.30.Ik
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(Integrable systems)
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03.65.Fd
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(Algebraic methods)
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04.20.Jb
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(Exact solutions)
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75.10.Jm
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(Quantized spin models, including quantum spin frustration)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245 and 11874393). |
Corresponding Authors:
Fa-Kai Wen
E-mail: fakaiwen@wipm.ac.cn
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Cite this article:
Fa-Kai Wen(温发楷) and Xin Zhang(张鑫) Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions 2021 Chin. Phys. B 30 050201
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[1] Gaudin M 1976 J. Phys. 37 1087
[2] Dukelsky J, Pittel S and Sierra G 2004 Rev. Mod. Phys. 76 643
[3] Deng H L and Fang X M 2008 Chin. Phys. B 17 702
[4] Richardson R W 1963 Phys. Lett. 3 277
[5] Richardson R W 1963 Phys. Lett. 5 82
[6] Richardson R W and Sherman N 1964 Nucl. Phys. 52 221
[7] Guan X W, Foerster A, Links J and Zhou H Q 2002 Nucl. Phys. B 642 501
[8] Faribault A, Koussir H and Mohamed M H 2019 Phys. Rev. B 100 205420
[9] Shen Y, Isaac P S and Links J 2020 SciPost Phys. Core 2 001
[10] Zhou H Q, Links J, Mackenzie R and Gould M D 2002 Phys. Rev. B 65 060502
[11] van den Berg R, Brandino G P, Araby O E, Konik R M, Gritsev V and Caux J S 2014 Phys. Rev. B 90 155117
[12] Rowlands D A and Lamacraft A 2018 Phys. Rev. Lett. 120 090401
[13] Ashida Y, Shi T, Schmidt R, Sadeghpour H R, Cirac J I and Demler E 2019 Phys. Rev. Lett. 123 183001
[14] Hao K, Yang W L, Fan H, Liu S Y, Wu K, Yang Z Y and Zhang Y Z 2012 Nucl. Phys. B 862 835
[15] Bortz M and Stolze J 2007 Phys. Rev. B 76 014304
[16] Claeys P W, Baerdemacker S D, Araby O E and Caux J S 2018 Phys. Rev. Lett. 121 080401
[17] He W B, Chesi S, Lin H Q and Guan X W 2019 Phys. Rev. B 99 174308
[18] He W B and Guan X W 2018 Chin. Phys. Lett. 35 110302
[19] Lu P, Shi H L, Cao L, Wang X H, Yang T, Cao J and Yang W L 2020 Phys. Rev. B 101 184307
[20] Hikami K, Kulish P P and Wadati M 1992 J. Phys. Soc. Jpn. 61 3071
[21] Hikami K 1995 J. Phys. A 28 4997
[22] Cao J P, Hou B Y and Yue R H 2001 Chin. Phys. 10 924
[23] Yang W L, Zhang Y Z and Gould M 2004 Nucl. Phys. B 698 503
[24] Cirilo Antonio N, Manojlovic N and Salom I 2014 Nucl. Phys. B 889 87
[25] Dzyaloshinskii I 1958 J. Phys. Chem. Solids 4 241
[26] Moriya T 1960 Phys. Rev. 120 91
[27] Kaplan T A 1983 Z. Phys. B 49 313
[28] Shekhtman L, Entin-Wohlman O and Aharony A 1992 Phys. Rev. Lett. 69 836
[29] Cao J, Yang W L, Shi K and Wang Y 2013 Phys. Rev. Lett. 111 137201
[30] Wang Y, Yang W L, Cao J and Shi K 2015 Off-Diagonal Bethe Ansatz for Exactly Solvable Models (Berlin: Springer-Verlag)
[31] Hao K, Cao J, Yang T and Yang W L 2015 Annals Phys. 354 401
[32] Faribault A and Tschirhart H 2017 SciPost Phys. 3 009
[33] Salom I, Manojlovic N and Cirilo Antonio N 2019 Nucl. Phys. B 939 358
[34] Manojlovic N and Salom I 2020 Symmetry 12 352
[35] Wen F, Yang T, Yang Z Y, Cao J, Hao K and Yang W L 2017 Nucl. Phys. B 915 119
[36] Sklyanin E K 1988 J. Phys. A: Math. Gen. 21 2375
[37] Zhang X, Li Y Y, Cao J, Yang W L, Shi K and Wang Y 2015 J. Stat. Mech. P05014
[38] Zhang X, Li Y Y, Cao J, Yang W L, Shi K and Wang Y 2015 Nucl. Phys. B 893 70
[39] Nepomechie R I and Wang C 2014 J. Phys. A 47 032001 |
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