Continuous Quantum Phase Transitions

TL;DR

This paper explores continuous quantum phase transitions, highlighting their unique critical behaviors and how path integral methods reveal finite temperature scaling and quantum-classical crossover phenomena.

Contribution

It introduces a path integral framework for understanding quantum phase transitions, connecting quantum criticality with classical finite size scaling and dephasing length concepts.

Findings

Finite temperature behavior follows finite size scaling laws.

Quantum and classical fluctuations crossover is governed by a temperature-dependent dephasing length.

Application to Josephson junction arrays and quantum Hall systems demonstrates the theory's relevance.

Abstract

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. We show that considerable insight is gained by considering the path integral description of the quantum statistical mechanics of such systems, which takes the form of the {\em 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. We illustrate these ideas using Josephson junction arrays and with a set of recent experiments on phase transitions in systems exhibiting the quantum Hall effect.