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Decay of spin helices in XXZ quantum spin chains with single-ion anisotropy

Florian Lange1, Frank Göhmann2, Gerhard Wellein1, and Holger Fehske1,3

  • 1Erlangen National High Performance Computing Center, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
  • 2School of Mathematics and Natural Sciences, University of Wuppertal, 42097 Wuppertal, Germany
  • 3Institute of Physics, University of Greifswald, 17489 Greifswald, Germany

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Phys. Rev. B 113, 245401 – Published 1 June, 2026

DOI: https://doi.org/10.1103/mqvf-wq91

Abstract

Long-lived spin-helix states facilitate the study of nonequilibrium dynamics in quantum magnets. We consider the decay of transverse spin helices in antiferromagnetic spin-S XXZ chains with single-ion anisostropy. The spin-helix decay is observable in the time evolution of the local magnetization that we calculate numerically for the system in the thermodynamic limit using infinite time-evolving block decimation simulations. Although the single-ion anisotropy prevents helix states from being eigenstates of the Hamiltonian, they still can be long-lived for appropriately chosen wave numbers. In the case of easy-axis exchange anisotropy, the single-ion anisotropy may even stabilize the helices. Within a spin-wave approximation, we obtain a condition giving an estimate for the most stable wave number Q that agrees qualitatively with our numerical results.

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References (33)

  1. S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, and C. Gross, Far-from-equilibrium spin transport in Heisenberg quantum magnets, Phys. Rev. Lett. 113, 147205 (2014).
  2. P. N. Jepsen, Y. K. E. Lee, H. Lin, I. Dimitrova, Y. Margalit, W. W. Ho, and W. Ketterle, Long-lived phantom helix states in Heisenberg quantum magnets, Nat. Phys. 18, 899 (2022).
  3. P. N. Jepsen, W. W. Ho, J. Amato-Grill, I. Dimitrova, E. Demler, and W. Ketterle, Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms, Phys. Rev. X 11, 041054 (2021).
  4. V. Popkov, X. Zhang, and A. Klümper, Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains, Phys. Rev. B 104, L081410 (2021).
  5. X. Zhang, A. Klümper, and V. Popkov, Pedestrian's way to Baxter's Bethe ansatz for the periodic XYZ chain, Phys. Rev. B 109, 115411 (2024).
  6. V. Popkov, X. Zhang, F. Göhmann, and A. Klümper, Chiral basis for qubits and spin-helix decay, Phys. Rev. Lett. 132, 220404 (2024).
  7. X. Zhang, F. Göhmann, A. Klümper, and V. Popkov, Chiral eigenbases of the XX and XY quantum spin chains, Phys. Rev. B 111, 094437 (2025).
  8. S. Kühn, F. Gerken, L. Funcke, T. Hartung, P. Stornati, K. Jansen, and T. Posske, Quantum spin helices more stable than the ground state: Onset of helical protection, Phys. Rev. B 107, 214422 (2023).
  9. J. F. Rodriguez-Nieva, A. Schuckert, D. Sels, M. Knap, and E. Demler, Transverse instability and universal decay of spin spiral order in the Heisenberg model, Phys. Rev. B 105, L060302 (2022).
  10. F. Gerken, I. Runkel, C. Schweigert, and T. Posske, All product eigenstates in Heisenberg models from a graphical construction, Phys. Rev. Res. 7, L012008 (2025).
  11. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  12. S. Dooley, Robust quantum sensing in strongly interacting systems with many-body scars, PRX Quantum 2, 020330 (2021).
  13. S. Dooley, L. Johnston, P. Gormley, and B. Campbell, Perfect quantum state transfer through a chaotic spin chain via many-body scars, Phys. Rev. B 112, 214304 (2025).
  14. M. G. Sousa, R. F. P. Costa, G. D. de Morales Neto, and E. Vernek, Breakdown of thermalization in spin chains with single-ion anisotropy, Sci. Rep. 14, 25315 (2024).
  15. M. Zheng, C. Liang, S. Chen, and X. Zhang, Exact spin helix eigenstates in the anisotropic spin-s Heisenberg model with arbitrary dimensions, Phys. Rev. B 112, 165102 (2025).
  16. G. Zhang and Z. Song, Stable dynamic helix state in the nonintegrable XXZ Heisenberg model, Phys. Scr. 99, 075119 (2024).
  17. Q. Hu, W.-Y. Zhang, Y. Han, and W.-L. You, Krylov complexity in quantum many-body scars of spin-1 models, Phys. Rev. B 111, 165106 (2025).
  18. F. D. M. Haldane, Nonlinear field theory of large-spin Heisenberg antiferromagnets: Semiclassically quantized solitons of the one-dimensional easy-axis Néel state, Phys. Rev. Lett. 50, 1153 (1983).
  19. G.-H. Liu, W. Li, W.-L. You, G. Su, and G.-S. Tian, Entanglement spectrum and quantum phase transitions in one-dimensional S=1 XXZ model with uniaxial single-ion anisotropy, Physica B 443, 63 (2014).
  20. S. Ejima, T. Yamaguchi, F. H. L. Essler, F. Lange, Y. Ohta, and H. Fehske, Exotic criticality in the dimerized spin-1 XXZ chain with single-ion anisotropy, SciPost Phys. 5, 059 (2018).
  21. S. Ejima, F. Lange, and H. Fehske, Quantum criticality in dimerised anisotropic spin-1 chains, Eur. Phys. J.: Spec. Top. 230, 1009 (2021).
  22. V. Popkov, M. Žnidarič, and X. Zhang, Universality in the relaxation of spin helices under XXZ spin-chain dynamics, Phys. Rev. B 107, 235408 (2023).
  23. G. Vidal, Classical simulation of infinite-size quantum lattice systems in one spatial dimension, Phys. Rev. Lett. 98, 070201 (2007).
  24. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (NY) 326, 96 (2011).
  25. D. Bhowmick, V. B. Bulchandani, and W. W. Ho, Asymmetric decay of quantum many-body scars in XYZ quantum spin chains, arXiv:2505.05435.
  26. J. Schliemann and F. G. Mertens, Semiclassical description of Heisenberg models via spin-coherent states, J. Phys.: Condens. Matter 10, 1091 (1998).
  27. K. Tsuru, Spin waves in an easy-plane ferromagnet with single-ion anisotropy, J. Phys. C 19, 2031 (1986).
  28. Y. B. Shi and Z. Song, Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction, Phys. Rev. B 108, 085108 (2023).
  29. C.-J. Lin, A. Chandran, and O. I. Motrunich, Slow thermalization of exact quantum many-body scar states under perturbations, Phys. Rev. Res. 2, 033044 (2020).
  30. H.-R. Wang and D. Yuan, Generalized spin helix states as quantum many-body scars in partially integrable models, arXiv:2403.14755.
  31. D. Bhowmick and W. W. Ho, Granovskii-Zhedanov scar of XYZ spin-chain: Modern algebraic perspectives and realization in higher dimensional lattices, arXiv:2507.14895.
  32. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  33. M. Fishman, S. R. White, and E. M. Stoudenmire, Codebase release 0.3 for ITensor, SciPost Phys. Codebases 4-r0.3 (2022).

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Phys. Rev. B 113, 245401– Published 1 June, 2026
  • Received 30 November 2025
  • Revised 24 April 2026
  • Accepted 7 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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