Quantum Phase Transitions

  • Thomas Vojta
Chapter

Summary

Quantum phase transitions occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed. They are caused by quantum fluctuations which are a consequence of Heisenberg’s uncertainty principle. These lecture notes give a pedagogical introduction to quantum phase transitions. After collecting a few basic facts about phase transitions and critical behavior we discuss the importance of quantum mechanics and the relation between quantum and classical transitions as well as their experimental relevance. As a primary example we then consider the Ising model in a transverse field. We also briefly discuss quantum phase transitions in itinerant electron systems and their connection to non-Fermi liquid behavior.

Keywords

Dioxide Mercury Ferro Holmium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Andrews: Phil. Trans. R. Soc. 159, 575 (1869)CrossRefGoogle Scholar
  2. 2.
    K.G. Wilson: Phys. Rev. B 4, 3174 (1971); ibid. 3184Google Scholar
  3. 3.
    C. Pfleiderer, G.J. McMullan, G.G. Lonzarich: Physica B 206, 847 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    T. Vojta, D. Belitz, R. Narayanan, T.R. Kirkpatrick: Z. Phys. B 103, 451 (1997)ADSCrossRefGoogle Scholar
  5. D. Belitz, T.R. Kirkpatrick, T. Vojta: Phys. Rev. Lett. 82, 4707 (1999)ADSCrossRefGoogle Scholar
  6. 5.
    S.L. Sondhi, S.M. Girvin, J.P. Carini, D. Shahar: Rev. Mod. Phys. 69, 315 (1997)ADSCrossRefGoogle Scholar
  7. 6.
    T.R. Kirkpatrick, D. Belitz: `Quantum phase transitions in electronic systems’. In: Electron Correlations in the Solid State ed. by N.H. March (Imperial College Press, London 1999 )Google Scholar
  8. 7.
    T. Vojta: Ann. Phys. (Leipzig) 9, 403 (2000)ADSMATHCrossRefGoogle Scholar
  9. 8.
    S. Sachdev: Quantum Phase Transitions ( Cambridge University Press, Cambridge 2000 )MATHCrossRefGoogle Scholar
  10. 9.
    S.-K. Ma: Modern Theory of Critical Phenomena ( Benjamin, Reading 1976 )Google Scholar
  11. 10.
    N. Goldenfeld: Lectures on Phase Transitions and the Renormalization Group ( Addison—Wesley, Reading 1992 )Google Scholar
  12. 11.
    L.D. Landau: Phys. Z. Sowjetunion 11, 26 (1937); ibid. 545; Zh. Eksp. Teor. Fiz 7, 19 (1937); ibid. 627Google Scholar
  13. 12.
    L.P. Kadanoff: Physics 2, 263 (1966)Google Scholar
  14. 13.
    B. Widom: J. Chem. Phys. 43, 3892 (1965)ADSCrossRefGoogle Scholar
  15. 14.
    V.L. Ginzburg: Soy. Phys. Sol. State 2, 1824 (1960)MathSciNetGoogle Scholar
  16. 15.
    S. Chakravarty, B.I. Halperin, D.R. Nelson: Phys. Rev. B 39, 2344 (1989)ADSCrossRefGoogle Scholar
  17. 16.
    D. Bitko, T.F. Rosenbaum, G. Aeppli: Phys. Rev. Lett. 77, 940 (1996)ADSCrossRefGoogle Scholar
  18. 17.
    L.D. Landau: Zh. Eksp. Teor. Fiz. 30, 1058 (1956); ibid. 32, 59 (1957) [Soy. Phys. JETP 3, 920 (1956); ibid. 5, 101 (1957)]Google Scholar
  19. 18.
    M.B. Maple: J. Magn. Magn. Mater. 177, 18 (1998)ADSCrossRefGoogle Scholar
  20. 19.
    P. Coleman: Physica B 259, 353 (1999)ADSCrossRefGoogle Scholar
  21. 20.
    H. von Löhneysen: J. Phys. Condens. Matter 8, 9689 (1996)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thomas Vojta

There are no affiliations available

Personalised recommendations