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Duality and domain wall dynamics in a twisted Kitaev chain


The Ising chain in a transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, quantum criticality and duality. Although the quasi-one-dimensional ferromagnet CoNb2O6 has been regarded as the Ising chain’s best material realization, it exhibits substantial deviations from ideality. By combining terahertz spectroscopy and calculations, we show that CoNb2O6 is in fact described by a different model with bond-dependent interactions, which we call the ‘twisted Kitaev chain’, as these interactions are similar to those of the honeycomb Kitaev spin liquid. The ferromagnetic ground state of CoNb2O6 arises from the compromise between two axes. Owing to this frustration, even at zero field domain walls have quantum motion, which is described by the celebrated Su–Schriefer–Heeger model of polyacetylene and shows rich behaviour as a function of field. Nevertheless, close to the critical field, this model enters a universal regime in the Ising universality class. We observe that the excitation gap in the ferromagnet closes at a rate twice that of the paramagnet. This universal ratio originates in the Kramers–Wannier duality between domain walls and spin flips, and in the topological conservation of domain wall parity. Our work also shows that Co2+ magnets are fertile ground in the search for quantum spin liquids.

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Fig. 1: The Ising chain in a transverse field and the twisted Kitaev chain.
Fig. 2: TDTS data on CoNb2O6 and theoretical simulations of the twisted Kitaev chain spectral function.
Fig. 3: Evolution of CoNb2O6 in a transverse field.

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

Numerical simulations were performed with C++ code that makes use of the ITensor Software Library available at C++ and Python source codes are available from the corresponding authors on request.


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Work at Johns Hopkins University and Princeton University was supported as part of the Institute for Quantum Matter, an Energy Frontier Research Center funded by the Office of Basic Energy Sciences of the Department of Energy, under grant no. DE-SC0019331. Work at the University of Kentucky was supported by National Science Foundation award no. DMR-1611161. The work at the National Institute of Chemical Physics and Biophysics was supported by institutional research funding grant no. IUT23-3 of the Estonian Ministry of Education and Research and by European Regional Development Fund project no. TK134.

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Authors and Affiliations



C.M.M. performed the TDTS measurements. J.V., D.H., U.N. and T.R., performed the FTIR experiments. J.W.K., R.J.C., T.M.M. and S.M.K. grew the crystals. N.D. and R.K.K. performed the theoretical calculations. N.P.A. supervised the project. R.K. and N.P.A. wrote the paper with input from other authors.

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Correspondence to Ribhu K. Kaul or N. P. Armitage.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Jan Ravnik and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–8 and discussion.

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Morris, C.M., Desai, N., Viirok, J. et al. Duality and domain wall dynamics in a twisted Kitaev chain. Nat. Phys. 17, 832–836 (2021).

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