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Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field |
| Fa-Kai Wen(温发楷)1,2,3 and Kun Hao(郝昆)4,5,6,† |
1 College of Physics and Electronic Information, Yunnan Normal University, Kunming 650500, China;
2 Yunnan Key Laboratory of Opto-Electronic Information Technology, Kunming 650500, China;
3 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
4 Institute of Modern Physics, Northwest University, Xi'an 710127, China;
5 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China;
6 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China |
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Abstract The U(1) symmetry of the XXZ central spin model with an arbitrary central magnetic field B is broken, since its total spin in the z-direction is not conserved. We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method. The thermodynamic limit is investigated based on the solutions. We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N-1 scaling law, where N is the total number of spins. This result makes it possible to investigate the properties of the system in the thermodynamic limit. By assuming the structural form of the Bethe roots in the thermodynamic limit, we obtain the contribution of the direction of B to the ground state energy. It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit. This is the phenomenon caused by the U(1) symmetry breaking of the system.
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Received: 02 November 2022
Revised: 29 December 2022
Accepted manuscript online: 18 January 2023
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PACS:
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03.67.-a
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(Quantum information)
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02.30.Ik
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(Integrable systems)
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75.10.Pq
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(Spin chain models)
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42.50.Pq
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(Cavity quantum electrodynamics; micromasers)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245, 11874393, and 12134015), the Doctoral Scientific Research Foundation of Yunnan Normal University (Grant No. 00900205020503180), the National Natural Science Foundation of China (Grant Nos. 12275214, 11805152, 12047502, and 11947301), the Natural Science Basic Research Program of Shaanxi Province (Grant Nos. 2021JCW-19 and 2019JQ-107), and the Shaanxi Key Laboratory for Theoretical Physics Frontiers in China. |
Corresponding Authors:
Kun Hao
E-mail: haoke72@163.com
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Cite this article:
Fa-Kai Wen(温发楷) and Kun Hao(郝昆) Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field 2023 Chin. Phys. B 32 090307
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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] Dimo C and Faribault A 2022 Phys. Rev. B 105 L121404
[4] Ashida Y, Shi T, Schmidt R, Sadeghpour H R, Cirac J I and Demler E 2019 Phys. Rev. Lett. 123 183001
[5] Nepomechie R I and Gaun X W 2018 J. Stat. Mech. 2018 103104
[6] Tschirhart H, Platini T and Faribault A 2018 J. Stat. Mech. 2018 083102
[7] He W B, Chesi S, Lin H Q and Guan X W 2019 Phys. Rev. B 99 174308
[8] Liu J X, Shi H L, Shi Y H, Wang X H and Yang W L 2021 Phys. Rev. B 104 245418
[9] Shao L, Zhang R, Lu W, Zhang Z and Wang X 2023 Phys. Rev. A 107 013714
[10] Sklyanin E K 1988 J. Phys. A: Math. Gen. 21 2375
[11] Yang W L, Zhang Y Z and Gould M D 2004 Nucl. Phys. B 698 503
[12] Ortiz G, Somma R, Dukelsky J and Rombouts S 2005 Nucl. Phys. B 707 421
[13] Hao K, Cao J, Yang T and Yang W L 2015 Annals Phys. 354 401
[14] Claeys P W, De Baerdemacker S, Van Raemdonck M and Van Neck D 2015 J. Phys.: Conf. Ser. 597 012025
[15] Claeys P W, De Baerdemacker S, Van Raemdonck M and Van Neck D 2015 Phys. Rev. B 91 155102
[16] Hikami K 1995 J. Phys. A 28 4997
[17] Cirilo Antonio N, Manojlovic N and Salom I 2014 Nucl. Phys. B 889 87
[18] Faribault A, Araby O E, Strater C and Gritsev V 2011 Phys. Rev. B 83 235124
[19] Bortz M and Stolze J 2007 Phys. Rev. B 76 014304
[20] Ibanez M, Links J, Sierra G and Zhao S Y 2009 Phys. Rev. B 79 180501
[21] Pogosov W V, Shapiro D S, Bork L V and Onishchenko A I 2017 Nucl. Phys. B 919 218
[22] Shen Y, Isaac P S and Links J 2018 Nucl. Phys. B 937 28
[23] Shen Y, Isaac P S and Links J 2020 SciPost Phys. Core 2 001
[24] Claeys P W, Dimo C, Baerdemacker S D and Faribault A 2019 J. Phys. A 52 08LT01
[25] Wen F K and Zhang X 2021 Chin. Phys. B 30 050201
[26] Wang Y, Yang W L, Cao J and Shi K 2015 Off-Diagonal Bethe Ansatz for Exactly Solvable Models (Springer Press)
[27] Cao J, Yang W L, Shi K and Wang Y 2013 Phys. Rev. Lett. 111 137201
[28] Yang C N 1967 Phys. Rev. Lett. 19 1312
[29] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic Press)
[30] Wen F, Yang T, Yang Z Y, Cao J, Hao K and Yang W L 2017 Nucl. Phys. B 915 119
[31] Wen F, Yang Z Y, Yang T, Hao K, Cao J and Yang W L 2018 J. High Energy Phys. 06 076
[32] Xin Z, Qiao Y, Hao K, Cao J, Yang W L, Shi K and Wang Y 2018 Nucl. Phys. B 936 501
[33] Henkel M and Schutz G 1988 J. Phys. A 21 2617
[34] Li Y Y, Cao J, Yang W L, Shi K and Wang Y 2014 Nucl. Phys. B 884 17
[35] Pozsgay B and Rakos O 2018 J. Stat. Mech. 2018 113102
[36] Sun P, Xin Z R, Qiao Y, Hao K, Cao L, Cao J, Yang T and Yang W L 2019 J. Phys. A 52 265201 |
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