Quantum and classical phase transitions in double-layer quantum Hall ferromagnets

TL;DR

This paper investigates quantum and classical phase transitions in double-layer quantum Hall systems at odd filling factors, using a mapping to a classical XY model to analyze universal properties and transition temperatures.

Contribution

It introduces a mapping of the quantum Hall system's long-wavelength Lagrangian to a classical XY model, enabling analysis of phase transition properties and quantum fluctuation effects.

Findings

Universal properties of the quantum phase transition are determined by the mapping.

The dependence of the Kosterlitz-Thouless transition temperature on layer separation is characterized.

Quantum fluctuations significantly influence the transition temperature.

Abstract

We consider the problem of quantum and classical phase transitions in double-layer quantum Hall systems at $\nu=1/m$ (m odd integers) from a long-wavelength statistical mechanics viewpoint. We derive an explicit mapping of the long-wavelength Lagrangian of the quantum Hall system into that of a three-dimensional isotropic classical XY model whose coupling constant depends on the quantum fluctuation in the original quantum Hall Hamiltonian. Universal properties of the quantum phase transition at the critical layer separation are completely determined by this mapping. The dependence of the Kosterlitz-Thouless transition temperature on layer separation, including quantum fluctuation effects, is approximately obtained by simple finite-size scaling analyses.