Exact solution of an integrable quantum spin chain with competing interactions
Jian Wang(王健)1,2, Yi Qiao(乔艺)1,†, Junpeng Cao(曹俊鹏)1,2,3,4,‡, and Wen-Li Yang(杨文力)4,5,6,7,§
1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; 3 Songshan Lake Materials Laboratory, Dongguan 523808, China; 4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China; 5 Institute of Modern Physics, Northwest University, Xi'an 710127, China; 6 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China; 7 School of Physics, Northwest University, Xi'an 710127, China
Abstract We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T-Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.
(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))
Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0300600 and 2016YFA0302104), the National Natural Science Foundation of China (Grant Nos. 12074410, 11934015, 11975183, 11947301, and 11774397), the Major Basic Research Program of Natural Science of Shaanxi Province, China (Grant Nos. 2017KCT-12 and 2017ZDJC-32), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000), and the Fellowship of China Postdoctoral Science Foundation (Grant No. 2020M680724).
Corresponding Authors:
Yi Qiao, Junpeng Cao, Wen-Li Yang
E-mail: qiaoyi_joy@foxmail.com;junpengcao@iphy.ac.cn;wlyang@nwu.edu.cn
Cite this article:
Jian Wang(王健), Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), and Wen-Li Yang(杨文力) Exact solution of an integrable quantum spin chain with competing interactions 2021 Chin. Phys. B 30 117501
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