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Quantum criticality


As we mark the centenary of Albert Einstein's seminal contribution to both quantum mechanics and special relativity, we approach another anniversary — that of Einstein's foundation of the quantum theory of solids. But 100 years on, the same experimental measurement that puzzled Einstein and his contemporaries is forcing us to question our understanding of how quantum matter transforms at ultra-low temperatures.

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Figure 1
Figure 2: Schematic illustration of a quantum critical point showing the phase diagram (a) and the growth of droplets of quantum critical matter near the quantum critical point (b).
Figure 3: ‘Singularity in the phase diagram’ illustrated by data taken from the material YbRh2Si2 where an applied magnetic field tunes the material to a quantum critical point25.

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  1. Pais, A. Subtle is the Lord: the Science and the Life of Albert Einstein Ch. 20. 389–401 (Oxford Univ. Press, Oxford, 1982).

    Google Scholar 

  2. Domb, C. The Critical Point: a Historical Introduction to the Modern Theory of Critical Phenomena (Taylor & Francis, London, 1996).

    Google Scholar 

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

    MATH  Google Scholar 

  4. Hertz, J. Quantum critical phenomena. Phys. Rev. B 14, 1165–1184 (1976).

    Article  ADS  CAS  Google Scholar 

  5. Laughlin, R. B., Lonzarich, G. G., Monthoux, P. & Pines, D. The quantum criticality conundrum. Adv. Phys. 50, 361–365. (2001).

    Article  ADS  CAS  Google Scholar 

  6. von Lohneysen, H. et al. Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability. Phys. Rev. Lett. 72, 3262–3265 (1994).

    Article  ADS  Google Scholar 

  7. Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001).

    Article  ADS  CAS  Google Scholar 

  8. Julian, S. R. et al. The normal states of magnetic d and f transition metals. J. Phys. Condens. Matt. 8, 9675–9688 (1996).

    Article  ADS  CAS  Google Scholar 

  9. Grigera, S. A. et al. Magnetic field tuned quantum criticality in the metallic ruthenate Sr3Ru2O7 . Science 294, 329–332 (2001).

    Article  ADS  CAS  Google Scholar 

  10. Doiron-Leyraud, N. et al. Fermi liquid breakdown in the paramagnetic phase of a pure metal. Nature 425, 595–599 (2003).

    Article  ADS  CAS  Google Scholar 

  11. Schröder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351–355 (2000).

    Article  ADS  Google Scholar 

  12. Millis, A. J. Effect of a non-zero temperature on quantum critical points in itinerant fermion systems. Phys. Rev. B 48, 7183–7196 (1993).

    Article  ADS  CAS  Google Scholar 

  13. Rosch, A. Interplay of disorder and spin fluctuations in the resistivity near a quantum critical point. Phys. Rev. Lett. 82, 4280–4283 (1999).

    Article  ADS  CAS  Google Scholar 

  14. Belitz, D., Kirkpatrick, T. R. & Rollühler, J. Breakdown of the perturbative renormalization group at certain quantum critical points. Phys. Rev. Lett. 93, 155701/1–4 (2004).

  15. Si, Q., Rabello, S., Ingersent K. & Smith, J. L. Locally critical quantum phase transitions in strongly correlated metals. Nature 413, 804–808 (2001).

    Article  ADS  CAS  Google Scholar 

  16. Coleman, P., Pépin, C., Qimiao Si & Ramazashvili, R. How do Fermi liquids get heavy and die? J. Phys. Condens. Matt. 13, R723–R738 (2001).

    Article  ADS  CAS  Google Scholar 

  17. Senthil, T., Vishwanath, A., Balents, L., Sachdev, S. & Fisher, M. P. A. Deconfined quantum critical points. Science 303, 1490–1494 (2004).

    Article  ADS  CAS  Google Scholar 

  18. Mathur, N. D. et al. Magnetically mediated superconductivity in heavy fermion compounds. Nature 394, 39–43 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Petrovic, C. et al. A new heavy-fermion superconductor CeIrIn/sub 5/: a relative of the cuprates? Europhys. Lett. 53, 354–359 (2001).

    Article  ADS  CAS  Google Scholar 

  20. Grigera, S. A. et al. Disorder-sensitive phase formation linked to metamagnetic quantum criticality. Science 306, 1154–1157 (2004).

    Article  ADS  CAS  Google Scholar 

  21. Kim, K. H., Harrison, N., Jaime, M., Boebinger, G. S. & Mydosh, J. A. Magnetic-field-induced quantum critical point and competing order parameters in URu2Si2 . Phys. Rev. Lett. 91, 256401/1–4 (2003).

  22. Amitsuka, H. et al. Hidden order and weak antiferromagnetism in URu2Si2 . Physica B 312–3, 390–396 (2002).

    Article  ADS  Google Scholar 

  23. Chandra, P. et al. Hidden orbital order in URu2Si2 . Nature 417, 831–834 (2002).

    Article  ADS  CAS  Google Scholar 

  24. Chapline, G. & Laughlin, R. B. in Artificial Black Holes (eds Novello, M. et al.) 179–198 (World Scientific, Singapore, 2002).

    Book  Google Scholar 

  25. Custers, J. et al. The break up of heavy electrons at a quantum critical point. Nature 424, 524–527 (2003).

    Article  ADS  CAS  Google Scholar 

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We gratefully acknowledge discussions with P. Chandra, Z. Fisk, A. P. Mackenzie and D. Pines. P.C. is supported by the National Science Foundation. A.J.S. is supported by the Royal Society, the Leverhulme Trust and the EPSRC.

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Coleman, P., Schofield, A. Quantum criticality. Nature 433, 226–229 (2005).

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