TY - JOUR

T1 - Continuous quantum phase transitions

AU - Sondhi, Shivaji Lal

AU - Girvin, S. M.

AU - Carini, J. P.

AU - Shahar, D.

PY - 1997/1

Y1 - 1997/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031482045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031482045&partnerID=8YFLogxK

U2 - https://doi.org/10.1103/revmodphys.69.315

DO - https://doi.org/10.1103/revmodphys.69.315

M3 - Article

VL - 69

SP - 315

EP - 333

JO - Reviews of Modern Physics

JF - Reviews of Modern Physics

SN - 0034-6861

IS - 1

ER -