Spin mapping, phase diagram, and collective modes in double layer quantum Hall systems at $\nu=2$

TL;DR

This paper simplifies the complex bilayer quantum Hall system at filling factor 2 using an exact spin mapping, revealing its phase diagram and collective excitations with improved understanding of its magnetic phases.

Contribution

It introduces an exact spin mapping that simplifies the hard-core boson description of the bilayer quantum Hall system at ν=2, providing precise phase diagram analysis.

Findings

Exact phase diagram matches previous approximate results.

Computed Goldstone-mode spectrum and Kosterlitz-Thouless temperature.

Identified the effective model as an easy-plane ferromagnet.

Abstract

An exact spin mapping is identified to simplify the recently proposed hard-core boson description (Demler and Das Sarma, Phys. Rev. Lett., to be published) of the bilayer quantum Hall system at filling factor 2. The effective spin model describes an easy-plane ferromagnet subject to an external Zeeman field. The phase diagram of this effective model is determined exactly and found to agree with the approximate calculation of Demler and Das Sarma, while the Goldstone-mode spectrum, order parameter stiffness and Kosterlitz-Thouless temperature in the canted antiferromagnetic phase are computed approximately.