Skip to main content
SpringerLink
Log in

Quantum Critical Dynamics and Scaling in One-Dimensional Antiferromagnets

  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

For a number of quantum critical points in one dimension quantum field theory has provided exact results for the scaling of spatial and temporal correlation functions. Experimental realizations of these models can be found in certain quasi one dimensional antiferromagnetic materials. Measuring the predicted scaling laws experimentally presents formidable technical challenges. In many cases it only became possible recently, thanks to qualitative progress in the development of inelastic neutron scattering techniques and to the discovery of new model compounds. Here we review some of the recent experimental studies of this type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.

Similar content being viewed by others

Notes

  1. The Introduction section contains textbook information on quantum criticality and scaling. While there are plenty of good books and review articles on the subject, the author’s personal preference is for [3, 4, 62].

  2. An important and common case of zν ≡ 1 is when the Zeeman term commutes with the rest of the Hamiltonian [50], as, for example, in the Heisenberg model.

REFERENCES

  1. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971).

    Google Scholar 

  2. M. F. Collins, Magnetic Critical Scattering (Oxford Univ. Press, Oxford, 1989).

    Google Scholar 

  3. S. Sachdev, Quantum Phase Transitions (Cambridge Univ. Press, Cambridge, 1999).

    MATH  Google Scholar 

  4. M. A. Continentino, Quantum Scaling in Many-Body Systems (World Scientific, Singapore, 2001).

    MATH  Google Scholar 

  5. G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering (Cambridge Univ. Press, Cambridge, 1978).

    Google Scholar 

  6. S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter (Clarendon, Oxford, 1984).

    Google Scholar 

  7. A. Tsvelik, Quantum Field Theory in Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 2007).

    MATH  Google Scholar 

  8. T. Giamarchi, Quantum Physics in One Dimension (Clarendon, Oxford,2003).

    MATH  Google Scholar 

  9. I. Affleck and F. D. M. Haldane, Phys. Rev. B 36, 5291 (1987).

    ADS  MathSciNet  Google Scholar 

  10. S. Yamamoto, Phys. Rev. B 51, 16128 (1995).

    ADS  Google Scholar 

  11. B. Lake, A. M. Tsvelik, S. Notbohm, D. Alan Tennant, T. G. Perring, M. Reehuis, C. Sekar, G. Krabbes, and B. Buchner, Nat. Phys. 6, 50 (2010).

    Google Scholar 

  12. T. Yankova, D. Huevonen, S. Muhlbauer, D. Schmidiger, E. Wulf, S. Zhao, A. Zheludev, T. Hong, V. O. Garlea, R. Custelcean, and G. Ehlers, arXiv: 1110.6375v1 (2011).

  13. F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980).

    ADS  MathSciNet  Google Scholar 

  14. T. Hikihara and A. Furusaki, Phys. Rev. B 63, 134438 (2001).

    ADS  Google Scholar 

  15. D. Schmidiger, P. Bouillot, S. Muehlbauer, S. Gvasaliya, C. Kollath, T. Giamarchi, and A. Zheludev, Phys. Rev. Lett. 108, 167201 (2012).

    ADS  Google Scholar 

  16. H. J. Schulz, Phys. Rev. Lett. 77, 2790 (1996).

    ADS  Google Scholar 

  17. O. Starykh, A. W. Sandvik, and R. R. P. Singh, Phys. B (Amsterdam, Neth.) 241–243, 563 (1998).

  18. D. C. Dender, P. R. Hammar, D. H. Reich, C. Broholm, and G. Aeppli, Phys. Rev. Lett. 79, 1750 (1997).

    ADS  Google Scholar 

  19. P. R. Hammar, M. B. Stone, D. H. Reich, C. Broholm, P. J. Gibson, M. M. Turnbull, C. P. Landee, and M. Oshikawa, Phys. Rev. B 59, 1008 (1999).

    ADS  Google Scholar 

  20. D. C. Dender, Ph.D. Thesis (Johns Hopkins Univ., Baltimore, MD, 1997).

  21. B. Lake, D. A. Tennant, C. D. Frost, and S. E. Nagler, Nat. Mater. 4, 329 (2005).

    ADS  Google Scholar 

  22. M. T. Hutchings, E. J. Samuelsen, G. Shirane, and K. Hirakawa, Phys. Rev. 188, 919 (1969).

    ADS  Google Scholar 

  23. S. Eggert and I. Affleck, Phys. Rev. B 46, 10866 (1992).

    ADS  Google Scholar 

  24. S. Fujimoto and S. Eggert, Phys. Rev. Lett. 92, 037206 (2004).

    ADS  Google Scholar 

  25. J. Sirker, S. Fujimoto, N. Laflorencie, S. Eggert, and I. Affleck, J. Stat. Mech.: Theory Exp. 2008, P02015 (2008).

  26. K. Karmakar and S. Singh, Phys. Rev. B 91, 224401 (2015).

    ADS  Google Scholar 

  27. G. Simutis, S. Gvasaliya, F. Xiao, C. P. Landee, and A. Zheludev, Phys. Rev. B 93, 094412 (2016).

    ADS  Google Scholar 

  28. G. Simutis, S. Gvasaliya, N. S. Beesetty, T. Yoshida, J. Robert, S. Petit, A. I. Kolesnikov, M. B. Stone, F. Bourdarot, H. C. Walker, D. T. Adroja, O. Sobolev, C. Hess, T. Masuda, A. Revcolevschi, B. Büchner, and A. Zheludev, Phys. Rev. B 95, 054409 (2017).

    ADS  Google Scholar 

  29. G. Simutis, Ph.D. Thesis (ETH, Zurich, 2016). https://doi.org/10.3929/ethz-a-010811102

  30. G. Simutis, S. Gvasaliya, M. Månsson, A. L. Chernyshev, A. Mohan, S. Singh, C. Hess, A. T. Savici, A. I. Kolesnikov, A. Piovano, T. Perring, I. Zaliznyak, B. Buchner, and A. Zheludev, Phys. Rev. Lett. 111, 067204 (2013).

    ADS  Google Scholar 

  31. M. Hälg, D. Hüvonen, N. P. Butch, F. Demmel, and A. Zheludev, Phys. Rev. B 92, 104416 (2015).

    ADS  Google Scholar 

  32. M. Haelg, Ph.D. Thesis (ETH, Zurich, 2015). https://doi.org/10.3929/ethz-a-010573756

  33. T. Hong, R. Custelcean, B. C. Sales, B. Roessli, D. K. Singh, and A. Zheludev, Phys. Rev. B 80, 132404 (2009).

    ADS  Google Scholar 

  34. T. Hong, Y. H. Kim, C. Hotta, Y. Takano, G. Tremelling, M. M. Turnbull, C. P. Landee, H.-J. Kang, N. B. Christensen, K. Lefmann, K. P. Schmidt, G. S. Uhrig, and C. Broholm, Phys. Rev. Lett. 105, 137207 (2010).

    ADS  Google Scholar 

  35. K. Ninios, T. Hong, T. Manabe, C. Hotta, S. N. Herringer, M. M. Turnbull, C. P. Landee, Y. Takano, and H. B. Chan, Phys. Rev. Lett. 108, 097201 (2012).

    ADS  Google Scholar 

  36. M. Jeong, H. Mayaffre, C. Berthier, D. Schmidiger, A. Zheludev, and M. Horvatić, Phys. Rev. Lett. 111, 106404 (2013).

    ADS  Google Scholar 

  37. K. Y. Povarov, D. Schmidiger, N. Reynolds, R. Bewley, and A. Zheludev, Phys. Rev. B 91, 020406 (2015).

    ADS  Google Scholar 

  38. M. Jeong, D. Schmidiger, H. Mayaffre, M. Klanjšek, C. Berthier, W. Knafo, G. Ballon, B. Vignolle, S. Krämer, A. Zheludev, and M. Horvatić, Phys. Rev. Lett. 117, 106402 (2016).

    ADS  Google Scholar 

  39. P. Bouillot, C. Kollath, A. M. Läuchli, M. Zvonarev, B. Thielemann, C. Rüegg, E. Orignac, R. Citro, M. Klanjšek, C. Berthier, M. Horvatić, and T. Giamarchi, Phys. Rev. B 83, 054407 (2011).

    ADS  Google Scholar 

  40. D. Schmidiger, S. Mühlbauer, S. N. Gvasaliya, T. Yankova, and A. Zheludev, Phys. Rev. B 84, 144421 (2011).

    ADS  Google Scholar 

  41. D. Schmidiger, Ph.D. Thesis (ETH, Zurich, 2014). https://doi.org/10.3929/ethz-a-010379214

  42. D. Schmidiger, P. Bouillot, T. Guidi, R. Bewley, C. Kollath, T. Giamarchi, and A. Zheludev, Phys. Rev. Lett. 111, 107202 (2013).

    ADS  Google Scholar 

  43. D. Schmidiger, P. Bouillot, G. Ehlers, S. Muhlbauer, A. M. Tsvelik, C. Kollath, T. Giamarchi, and A. Zheludev, Phys. Rev. B 88, 094411 (2013).

    ADS  Google Scholar 

  44. E. G. Batyev and L. S. Braginski, Sov. Phys. JETP 60, 781 (1984).

    Google Scholar 

  45. D. Blosser, V. K. Bhartiya, D. J. Voneshen, and A. Zheludev, Phys. Rev. Lett. 121, 247201 (2018).

    ADS  Google Scholar 

  46. S. Sachdev, T. Senthil, and R. Shankar, Phys. Rev. B 50, 258 (1994).

    ADS  Google Scholar 

  47. I. Affleck, Phys. Rev. B 41, 6697 (1990).

    ADS  Google Scholar 

  48. I. Affleck, Phys. Rev. B 43, 3215 (1991).

    ADS  Google Scholar 

  49. E. S. Sorensen and I. Affleck, Phys. Rev. Lett. 71, 1633 (1993).

    ADS  Google Scholar 

  50. S. Sachdev, Zeitschr. Phys. B: Condens. Matter 94, 469 (1994).

    ADS  Google Scholar 

  51. O. Breunig, M. Garst, A. Klümper, J. Rohrkamp, M. M. Turnbull, and T. Lorenz, Sci. Adv. 3 (2017). https://doi.org/10.1126/sciadv.aao3773

  52. D. Blosser, Ph.D. Thesis (ETH, Zurich, 2019).

  53. D. Blosser, N. Kestin, K. Y. Povarov, R. Bewley, E. Coira, T. Giamarchi, and A. Zheludev, Phys. Rev. B 96, 134406 (2017).

    ADS  Google Scholar 

  54. V. E. Korepin and N. A. Slavnov, Commun. Math. Phys. 129, 103 (1990)

    ADS  Google Scholar 

  55. M. Hälg, W. E. A. Lorenz, K. Y. Povarov, M. Mansson, Y. Skourski, and A. Zheludev, Phys. Rev. B 90, 174413 (2014).

    ADS  Google Scholar 

  56. T. Barnes and J. Riera, Phys. Rev. B 50, 6817 (1994).

    ADS  Google Scholar 

  57. S. Sachdev, Nucl. Phys. B 464, 576 (1996).

    ADS  Google Scholar 

  58. M. Hälg, D. Hüvonen, T. Guidi, D. L. Quintero-Castro, M. Boehm, L. P. Regnault, M. Hagiwara, and A. Zheludev, Phys. Rev. B 92, 014412 (2015).

    ADS  Google Scholar 

  59. R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Science (Washington, DC, U. S.) 327, 177 (2010).

    ADS  Google Scholar 

  60. A. Zheludev, T. Masuda, B. Sales, D. Mandrus, T. Papenbrock, T. Barnes, and S. Park, Phys. Rev. B 69, 144417 (2004).

    ADS  Google Scholar 

  61. L. P. Regnault, A. Zheludev, M. Hagiwara, and A. Stunault, Phys. Rev. B 73, 174431 (2006).

    ADS  Google Scholar 

  62. J. Cadry, Scaling and Renormalization in Statistical Physics (Cambridge Univ. Press, Cambridge, 2003).

    Google Scholar 

Download references

ACKNOWLEDGMENTS

Most of the new experimental material reviewed here was supported by the Swiss National Science Foundation, Division 2, and is the subject of successfully defended PhD dissertations at ETH Zurich, namely those of Dr. David Schmidiger [41], Dr. Manuel Haelg [32], Dr. Gediminas Simutis [29] and Dr. Dominic Blosser [52]. K. Povarov, S. Gvasaliya, W. Lorentz and D. Huevonen (ETH Zurich) also played an important role in many of the measurements. Which, in turn, would be impossible without the expert support of instrument scientists at neutron scattering user facilities: T. Perring, D. Voneshen, R. Bewley, H.C. Walker, D.T. Adjora, F. Demmel and T. Guidi (Rutherford Appleton Laboratory, UK); J. Robert and S. Petit (Laboratoire Leon Brillouin, CEA-CNRS, Saclay, France); M. Stone, A.I. Kolesnikov and A.T. Savichi (Oak Ridge National Laboratory, USA); L.P. Regnault and F. Bourdarot (CEA Grenoble, France); O. Sobolev (Forschungsneutronenquelle Heinz Maier-Leibnitz, Munich, Germany); N.P. Butch (National Institute of Standards and Technology, USA); D.L. Quintero-Castro (Helmholtz-Zentrum Berlin, Germany); A. Piovano and M. Boehm (Institut Laue-Langevin, Grenoble, France). While most samples for the described experiments were grown at ETH Zürich, the linear-chain cuprate crystals originate from the laboratories of Prof. B. Buechner (IFW Dresden, Germany), Prof. T. Masuda (The University of Tokyo, Japan) and Prof. A. Revcolevschi (Universite Paris-Sud, Orsay, France).

Author information

Authors and Affiliations

  1. ETH Zürich, 8093, Zürich, Switzerland

    A. Zheludev

Authors
  1. A. Zheludev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Zheludev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheludev, A. Quantum Critical Dynamics and Scaling in One-Dimensional Antiferromagnets. J. Exp. Theor. Phys. 131, 34–45 (2020). https://doi.org/10.1134/S1063776120070183

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776120070183

Search

Navigation