Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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

### Subjects

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

## 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.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Defect-induced ferromagnetism in a S = 1/2 quasi-one-dimensional Heisenberg antiferromagnetic chain compound

Scientific Reports Open Access 14 July 2021

• ### Spin dynamics and Griffiths singularity in the random quantum Ising magnet PrTiNbO6

npj Quantum Materials Open Access 31 March 2021

• ### Spinon confinement and a sharp longitudinal mode in Yb2Pt2Pb in magnetic fields

Nature Communications Open Access 08 March 2019

## Access options

\$32.00

All prices are NET prices.

## 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).

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).

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

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).

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).

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).

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).

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

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).

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

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

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).

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

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).

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

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

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).

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).

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).

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).

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

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).

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).

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

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).

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

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

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).

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

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

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).

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).

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

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

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

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

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).

## 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.

## Author information

Authors

### Contributions

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.

### Corresponding authors

Correspondence to Virginie Simonet or Thierry Giamarchi.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Figures 1–7, Supplementary References

## Rights and permissions

Reprints and Permissions

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

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41567-018-0126-8

• ### Detection of Kardar–Parisi–Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain

• A. Scheie
• N. E. Sherman
• D. A. Tennant

Nature Physics (2021)

• ### Spin dynamics and Griffiths singularity in the random quantum Ising magnet PrTiNbO6

• Yuesheng Li
• Qiao-Yi Li

npj Quantum Materials (2021)

• ### Defect-induced ferromagnetism in a S = 1/2 quasi-one-dimensional Heisenberg antiferromagnetic chain compound

• Zhe Wang
• Lin Hu
• Zhe Qu

Scientific Reports (2021)

• ### Unconventional magnetic excitations and spin dynamics of exotic quantum spin systems BaCo$$_2$$V$$_2$$O$$_8$$ and Ba$$_3$$CuSb$$_2$$O$$_9$$

• Yibo Han
• Shojiro Kimura
• Masayuki Hagiwara

Applied Magnetic Resonance (2021)

• ### Spinon confinement and a sharp longitudinal mode in Yb2Pt2Pb in magnetic fields

• W. J. Gannon
• I. A. Zaliznyak
• M. C. Aronson

Nature Communications (2019)