Abstract

When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided1. Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids2. However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum3,4,5. Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu2PO6, we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.

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Acknowledgements

We would also like to thank G. Uhrig, O. Tchernyshyov and S. K. Kim for helpful discussions. This research was supported by NSERC of Canada, Canada Foundation for innovation, Canada Research Chairs Program, and Centre for Quantum Materials at the University of Toronto. Work at ORNL was sponsored by the Division of Scientific User Facilities, Office of Basic Energy Science, US Department of Energy (DOE). Work at NIST utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-0944772.

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Affiliations

  1. Department of Physics and Center for Quantum Materials, University of Toronto, Toronto, Ontario M5S 1A7, Canada

    • K. W. Plumb
    • , Kyusung Hwang
    • , Yong Baek Kim
    •  & Young-June Kim
  2. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    • Y. Qiu
    •  & Leland W. Harriger
  3. Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA

    • Y. Qiu
  4. Neutron Data Analysis and Visualization Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • G. E. Granroth
  5. Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • Alexander I. Kolesnikov
  6. Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan

    • G. J. Shu
    •  & F. C. Chou
  7. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH–5232 Villigen, Switzerland

    • Ch. Rüegg
  8. Department of Quantum Matter Physics, University of Geneva, CH–1211 Geneva, Switzerland

    • Ch. Rüegg
  9. Canadian Institute for Advanced Research/Quantum Materials Program, Toronto, Ontario MSG 1Z8, Canada

    • Yong Baek Kim

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Contributions

K.W.P. and Y.-J.K. conceived the experiments. K.W.P., Y.Q., L.W.H. G.E.G. and A.I.K. performed the experiments and K.W.P. analysed the data. C.R. provided additional data. K.H. and Y.B.K. developed the theoretical model and performed calculations. G.J.S. and F.C.C. provided the sample. K.W.P. and Y.-J.K. wrote the paper with contributions from all co-authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Young-June Kim.

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DOI

https://doi.org/10.1038/nphys3566

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