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  • Letter
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Topological quantum phase transition in the Ising-like antiferromagnetic spin chain BaCo2V2O8

A Publisher Correction to this article was published on 12 July 2018

This article has been updated

Abstract

Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations have been at the heart of our understanding of a whole novel class of phase transitions. In most cases, those transitions are controlled by a single type of topological objects. There are, however, some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realizations of such cases is thus of considerable interest. We show here that this situation occurs in BaCo2V2O8, a spin-1/2 Ising-like quasi-one-dimensional antiferromagnet, when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological object, which are captured by different components of the dynamical structure factor.

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Fig. 1: BaCo2V2O8 at zero field.
Fig. 2: Static properties in a transverse magnetic field.
Fig. 3: Magnetic excitations in a transverse magnetic field.
Fig. 4: Two dual topological objects.

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Change history

  • 12 July 2018

    In the version of this Letter originally published, the year for ref. 30 was incorrectly listed as 2009; it should have been 2004. This has now been corrected.

References

  1. Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems. Sov. Phys. JETP 32, 493–500 (1971).

    ADS  MathSciNet  Google Scholar 

  2. Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems. Sov. Phys. JETP 34, 610–616 (1972).

    ADS  Google Scholar 

  3. Kosterlitz, J. M. & Thouless, D.J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973).

    Article  ADS  Google Scholar 

  4. José, J. V. 40 Years of Berezinskii–Kosterlitz–Thouless Theory (World Scientific, Indiana University, Bloomington, IN, 2013).

  5. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, Oxford, 2004).

    MATH  Google Scholar 

  6. Haldane, F. D. M. Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model. Phys. Lett. A 93, 464–468 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  7. Haldane, F. D. M. Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state. Phys. Rev. Lett. 50, 1153–1156 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  8. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  ADS  Google Scholar 

  9. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  Google Scholar 

  10. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  11. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    Article  ADS  Google Scholar 

  12. Kosterlitz, J. M . The critical properties of the two-dimensional xy model. J. Phys. C 7, 1046–1060 (1974).

    Article  ADS  Google Scholar 

  13. Rajaraman, R. Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (Amsterdam, North Holland, 1982).

  14. José, J. V., Kadanoff, L. P., Kirkpatrick, S. & Nelson, D. R. Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B 16, 1217–1241 (1977).

    Article  ADS  Google Scholar 

  15. Fertig, H. A. Deconfinement in the two-dimensional XY model. Phys. Rev. Lett. 89, 035703 (2002).

    Article  ADS  Google Scholar 

  16. Giamarchi, T. & Schulz, H.J. Theory of spin-anisotropic electron–electron interactions in quasi-one dimensional metals. J. Phys. Fr. 49, 819–835 (1988).

    Article  Google Scholar 

  17. Lecheminant, P., Gogolin, A. O. & Nersesyan, A. A. Criticality in self-dual sine-Gordon models. Nucl. Phys. B 639, 502–523 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  18. He, Z., Fu, D., Kyômen, T., Taniyama, T. & Itoh, M. Crystal growth and magnetic properties of BaCo2V2O8. Chem. Mater. 17, 2924–2926 (2005).

    Article  Google Scholar 

  19. Kimura, S. et al. Novel ordering of an S = 1/2 quasi-1D Ising-like antiferromagnet in magnetic field. Phys. Rev. Lett. 100, 057202 (2008).

    Article  ADS  Google Scholar 

  20. Canévet, E. et al. Field-induced magnetic behavior in quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8: A single-crystal neutron diffraction study. Phys. Rev. B 87, 054408 (2013).

    Article  ADS  Google Scholar 

  21. Kimura, S. et al. Collapse of magnetic order of the quasi one-dimensional Ising-like antiferromagnet BaCo2V2O8 in transverse fields. J. Phys. Soc. Jpn 82, 033706 (2013).

    Article  ADS  Google Scholar 

  22. Niesen, S. K. et al. Magnetic phase diagrams, domain switching, and quantum phase transition of the quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8. Phys. Rev. B 87, 224413 (2013).

    Article  ADS  Google Scholar 

  23. Kimura, S. et al. High field magnetism of the quasi one-dimensional anisotropic antiferromagnet BaCo2V2O8. J. Phys. Conf. Ser. 51, 99–102 (2006).

    Article  ADS  Google Scholar 

  24. Kimura, S. et al. Field-induced order–disorder transition in antiferromagnetic BaCo2V2O8 driven by a softening of spinon excitation. Phys. Rev. Lett. 99, 087602 (2007).

    Article  ADS  Google Scholar 

  25. Grenier, B. et al. Longitudinal and transverse Zeeman ladders in the Ising-like chain antiferromagnet BaCo2V2O8. Phys. Rev. Lett. 114, 017201 (2015); erratum 115, 119902 (2015).

  26. Ishimura, N. & Shiba, H. Dynamical correlation functions of one-dimensional anisotropic Heisenberg model with spin l/2. Prog. Theor. Phys. 63, 743–758 (1980).

    Article  ADS  Google Scholar 

  27. Wang, Z. et al. Spinon confinement in the one-dimensional Ising-like antiferromagnet SrCo2V2O8. Phys. Rev. B 91, 140404(R) (2015).

    Article  ADS  Google Scholar 

  28. Wang, Z. et al. From confined spinons to emergent fermions: observation of elementary magnetic excitations in a transverse-field Ising chain. Phys. Rev. B 94, 125130 (2016).

    Article  ADS  Google Scholar 

  29. Bera, A. K. et al. Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet. Phys. Rev. B 96, 054423 (2017).

    Article  ADS  Google Scholar 

  30. Sato, M. & Oshikawa, M. Coupled S=1/2 Heisenberg antiferromagnetic chains in an effective staggered field. Phys. Rev. B 69, 054406 (2004).

    Article  ADS  Google Scholar 

  31. Okutani, A., Kimura, S., Takeuchi, T. & Hagiwara, M. High-field multi-frequency ESR in the quasi-1D = 1/2 Ising-like antiferromagnet BaCo2V2O8 in a transverse field. Appl. Magn. Reson. 46, 1003–1006 (2015).

    Article  Google Scholar 

  32. Vidal, G. Classical simulation of infinite-size quantum lattice systems in one spatial dimension. Phys. Rev. Lett. 98, 070201 (2007).

    Article  ADS  Google Scholar 

  33. Phien, H. N., Vidal, G. & McCulloch, I. P. Infinite boundary conditions for matrix product state calculations. Phys. Rev. B 86, 245107 (2012).

    Article  ADS  Google Scholar 

  34. Affleck, I. & Oshikawa, M. Field-induced gap in Cu benzoate and other S = 1/2 antiferromagnetic chains. Phys. Rev. B 60, 1038–1056 (1999).

    Article  ADS  Google Scholar 

  35. Berg, E., Dalla Torre, E., Giamarchi, T. & Altman, E. Rise and fall of hidden string order of lattice bosons. Phys. Rev. B 77, 245119 (2008).

    Article  ADS  Google Scholar 

  36. Endres, M. et al. Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334, 200–203 (2011).

    Article  ADS  Google Scholar 

  37. Tsvelik, A. M. & Kuklov, A. B. Parafermion excitations in a superfluid of quasi-molecular chains. New. J. Phys. 14, 115033 (2012).

    Article  ADS  Google Scholar 

  38. Lejay, P. et al. Crystal growth and magnetic property of MCo2V2O8 (M = Sr and Ba). J. Cryst. Growth 317, 128–131 (2011).

    Article  ADS  Google Scholar 

  39. Boehm, M. et al. ThALES–three axis low energy spectroscopy for highly correlated electron systems. Neutron News 26, 18–21 (2015).

    Article  Google Scholar 

  40. Schmalzl, K. et al. The upgrade of the cold neutron three-axis spectrometer IN12 at the ILL. Nucl. Instrum. Methods Phys. Res. A 819, 89–98 (2016).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank R. Ballou, C. Berthier, M. Horvatić, M. Klanjšek and S. Niesen for fruitful discussions, P. Courtois and R. Silvestre for their help in the sample co-alignment carried out at ILL before the experiment at PSI, E. Villard, B. Vettard and M. Bartkowiak for their technical support during the INS experiments on ThALES (ILL), IN12 (ILL) and TASP (PSI), respectively, and J. Debray, A. Hadj-Azzem and J. Balay for their contribution to the crystal growth, cut and orientation. We acknowledge ILL and PSI for allocating neutron beam time. This work was partly supported by the French ANR Project DYMAGE (ANR-13-BS04-0013). S.T. is supported by the Swiss National Science Foundation under Division II and ImPACT project (no. 2015-PM12-05-01) from the Japan Science and Technology Agency. M.M. acknowledges funding from the Swedish Research Council (VR) through a neutron project grant (Dnr 2016-06955). T.L. acknowledges support by the Deutsche Forschungsgemeinschaft through CRC 1238 Project A02. S.C.F. is supported by JSPS KAKENHI grant no. 16J04731.

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All authors contributed significantly to this work. In detail, sample preparation was performed by P.L., neutron scattering experiments and analysis were carried out by Q.F., B.G., S.P. and V.S. with the support of S.R., L.-P.R., M.B., J.S.W., M.M. and C.R., calculations were performed by S.T., S.C.F. and T.G., inputs for the discussion of the physical results were provided by C.R., B.C. and T.L.; the manuscript was written by V.S., S.P., B.G., Q.F., T.G. and S.T. with constant feedback from the other co-authors.

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Correspondence to Virginie Simonet or Thierry Giamarchi.

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Faure, Q., Takayoshi, S., Petit, S. et al. Topological quantum phase transition in the Ising-like antiferromagnetic spin chain BaCo2V2O8. Nature Phys 14, 716–722 (2018). https://doi.org/10.1038/s41567-018-0126-8

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