Quantum phase transitions: introduction and some open problems

Achim Rosch

in Quantum Theory from Small to Large Scales

Published in print May 2012 | ISBN: 9780199652495
Published online September 2012 | e-ISBN: 9780191741203 | DOI:

Series: Lecture Notes of the Les Houches Summer School

Quantum phase transitions: introduction and some open problems

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At a quantum critical point the ground state of a many-particle quantum system undergoes a phase transition when some control parameters such as pressure, magnetic field, or chemical composition is varied. The universal behaviour characteristic for such quantum phase transitions often affects a wide temperature range and gives rise to novel material properties. This chapter gives a short overview over five lectures held during the Les Houches summer school ‘Quantum theory from small to large scales’ in 2010. After an introductory chapter, field driven magnetic quantum phase transitions of insulators are used as an example to discuss some of the concepts underlying quantum phase transitions. Both experimentally and theoretically, quantum phase transitions in metals are much less understood compared to insulating systems. After a brief review of the standard approach to describe those systems, the importance of multiple time scales and associated multiple critical exponents z are discussed. Finally, emergent gauge theories close to critical points are investigated. As an example, it discusses why a gauge theory describes the (classical) phase transitions of a nematic, if topological defects are suppressed.

Keywords: quantum phase transitions; scaling; renormalization group; emergent gauge theories

Chapter.  8019 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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