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.
KeywordsIsing Model Critical Exponent Critical Behavior Quantum Phase Transition Fermi Liquid
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- 2.K.G. Wilson: Phys. Rev. B 4, 3174 (1971); ibid. 3184Google Scholar
- 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
- 9.S.-K. Ma: Modern Theory of Critical Phenomena ( Benjamin, Reading 1976 )Google Scholar
- 10.N. Goldenfeld: Lectures on Phase Transitions and the Renormalization Group ( Addison—Wesley, Reading 1992 )Google Scholar
- 11.L.D. Landau: Phys. Z. Sowjetunion 11, 26 (1937); ibid. 545; Zh. Eksp. Teor. Fiz 7, 19 (1937); ibid. 627Google Scholar
- 12.L.P. Kadanoff: Physics 2, 263 (1966)Google Scholar
- 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