Continuous quantum phase transitions

Rev. Mod. Phys. 69, 315 – Published 1 January 1997
S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar


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.


© 1997 The American Physical Society

Authors & Affiliations

S. L. Sondhi

  • Department of Physics, Princeton University, Princeton, New Jersey 08544

S. M. Girvin and J. P. Carini

  • Department of Physics, Indiana University, Bloomington, Indiana 47405

D. Shahar

  • Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544

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