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Ultracold Gases and Quantum InformationLecture Notes of the Les Houches Summer School in Singapore: Volume 91, July 2009$
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Christian Miniatura, Leong-Chuan Kwek, Martial Ducloy, Benoît Grémaud, Berthold-Georg Englert, Leticia Cugliandolo, Artur Ekert, and Kok Khoo Phua

Print publication date: 2011

Print ISBN-13: 9780199603657

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199603657.001.0001

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Quantum phase transitions

Quantum phase transitions

Chapter:
(p.356) 7 Quantum phase transitions
Source:
Ultracold Gases and Quantum Information
Author(s):

G. G. Batrouni

R. T. Scalettar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199603657.003.0007

This chapter discusses quantum phase transitions (QPT). It starts with a brief review of thermal phase transitions, critical exponents and scaling laws. The scaling laws are then generalized to the QPT case which is also illustrated with two specific examples. The first example that of the one-dimensional Ising model in a transverse magnetic field; the second is that of the bosonic Hubbard model. Quantum Monte Carlo is described briefly and mean field theory is introduced with the help of several examples and exercises.

Keywords:   quantum phase transition, critical exponents, scaling laws, quantum Monte Carlo, mean field theory

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