CONTINUOUS QUANTUM PHASE-TRANSITIONS

A quantum system can undergo a continuous phase transition at the abso lute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contra st to their classical finite-temperature counterparts, their dynamic a nd 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 sc aling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads natural ly to the notion of a temperature-dependent dephasing length that gove rns the crossover between quantum and classical fluctuations. Using th ese ideas, a scaling analysis of experiments on Josephson-junction arr ays and quantum-Hall-effect systems is presented.