中国物理B ›› 2026, Vol. 35 ›› Issue (3): 37503-037503.doi: 10.1088/1674-1056/ae3067

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Gapless and ordered phases in spin-1/2 Kitaev-XX-Gamma chain

Zebin Zhuang(庄泽彬)1 and Wang Yang(杨望)2,†   

  1. 1 Department of Physics, Imperial College London, London SW7 2BZ, UK;
    2 School of Physics, Nankai University, Tianjin 300071, China
  • 收稿日期:2025-09-26 修回日期:2025-12-01 接受日期:2025-12-23 出版日期:2026-02-11 发布日期:2026-03-19
  • 通讯作者: Wang Yang E-mail:wyang@nankai.edu.cn
  • 基金资助:
    This work is supported by the National Natural Science Foundation of China (Grant No. 12474476) and the Fundamental Research Funds for the Central Universities.

Gapless and ordered phases in spin-1/2 Kitaev-XX-Gamma chain

Zebin Zhuang(庄泽彬)1 and Wang Yang(杨望)2,†   

  1. 1 Department of Physics, Imperial College London, London SW7 2BZ, UK;
    2 School of Physics, Nankai University, Tianjin 300071, China
  • Received:2025-09-26 Revised:2025-12-01 Accepted:2025-12-23 Online:2026-02-11 Published:2026-03-19
  • Contact: Wang Yang E-mail:wyang@nankai.edu.cn
  • Supported by:
    This work is supported by the National Natural Science Foundation of China (Grant No. 12474476) and the Fundamental Research Funds for the Central Universities.

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摘要： We study the spin-1/2 Kitaev chain with additional XX and symmetric off-diagonal Gamma interactions. By combining the Jordan-Wigner transformation with density matrix renormalization group (DMRG) numerical simulations, we obtain the exact solution of the model and map out the phase diagram containing six distinct phases. The four gapped phases display ferromagnetic and antiferromagnetic magnetic orders along the $(1,1,0)$- and $(1,-1,0)$-spin directions, whereas in the gapless phases, the low-energy spectrum consists of two branches of helical Majorana fermions with unequal velocities. The transition lines separating different phases include deconfined quantum critical lines with dynamical critical exponent $z = 1$ and quadratic critical lines with $z = 2$. Our work reveals the rich interplay among symmetry, magnetic order, and quantum criticality in the Kitaev-XX-Gamma chain.

关键词: spin chain, magnetism, magnetic phase transition, quantum compass model

Abstract: We study the spin-1/2 Kitaev chain with additional XX and symmetric off-diagonal Gamma interactions. By combining the Jordan-Wigner transformation with density matrix renormalization group (DMRG) numerical simulations, we obtain the exact solution of the model and map out the phase diagram containing six distinct phases. The four gapped phases display ferromagnetic and antiferromagnetic magnetic orders along the $(1,1,0)$- and $(1,-1,0)$-spin directions, whereas in the gapless phases, the low-energy spectrum consists of two branches of helical Majorana fermions with unequal velocities. The transition lines separating different phases include deconfined quantum critical lines with dynamical critical exponent $z = 1$ and quadratic critical lines with $z = 2$. Our work reveals the rich interplay among symmetry, magnetic order, and quantum criticality in the Kitaev-XX-Gamma chain.

Key words: spin chain, magnetism, magnetic phase transition, quantum compass model

中图分类号:  (Spin chain models)

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