Continuous quantum phase transitions

Shivaji Lal Sondhi, S. M. Girvin, J. P. Carini, D. Shahar

Research output: Contribution to journalArticlepeer-review

1101 Scopus citations


A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.

Original languageEnglish (US)
Pages (from-to)315-333
Number of pages19
JournalReviews of Modern Physics
Issue number1
StatePublished - Jan 1997

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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