Letter | Published:

Experimental observation of Bethe strings

Nature volume 554, pages 219223 (08 February 2018) | Download Citation


Almost a century ago, string states—complex bound states of magnetic excitations—were predicted to exist in one-dimensional quantum magnets1. However, despite many theoretical studies2,3,4,5,6,7,8,9,10,11, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg–Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz1,3,4. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe’s result1 is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

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We thank I. Bloch, M. Karbach, T. Lorenz and X. Zotos for discussions. We acknowledge partial support by the DFG via the Transregional Collaborative Research Center TRR 80, and by the HFML-RU/FOM and the HLD-HZDR, members of the European Magnetic Field Laboratory (EMFL). J.W., W.Y., S.X. and C.W. are supported by NSF grant number DMR-1410375 and AFOSR grant number FA9550-14-1-0168. C.W. also acknowledges partial support from the National Natural Science Foundation of China (grant number 11729402).

Author information

Author notes

    • Jianda Wu

    Present address: Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany.


  1. Experimental Physics V, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany

    • Zhe Wang
    •  & Alois Loidl
  2. Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany

    • Zhe Wang
  3. Department of Physics, University of California, San Diego, California 92093, USA

    • Jianda Wu
    • , Wang Yang
    • , Shenglong Xu
    •  & Congjun Wu
  4. Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany

    • Anup Kumar Bera
    • , A. T. M. Nazmul Islam
    •  & Bella Lake
  5. Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India

    • Anup Kumar Bera
  6. High Field Magnet Laboratory, Radboud University, 6525 ED Nijmegen, The Netherlands

    • Dmytro Kamenskyi
  7. Hochfeld Magnetlab Dresden, Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden, Germany

    • Joseph Matthew Law
  8. Institut für Festkörperphysik, Technische Universität Berlin, 10623 Berlin, Germany

    • Bella Lake


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Z.W. conceived and performed the optical experiments, analysed the data and coordinated the project. J.W., W.Y. and S.X. carried out the Bethe-ansatz calculations. A.K.B. and A.T.M.N.I. prepared and characterized the high-quality single crystals. A.K.B. and J.M.L. performed the high-field magnetization measurements. D.K. assisted with the high-field optical experiments. B.L., C.W. and A.L. supervised the project. Z.W., J.W., W.Y., C.W. and A.L. wrote the manuscript with input from all authors. All authors discussed the results.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Zhe Wang.

Reviewer Information Nature thanks M. Batchelor, J. van den Brink and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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