Bilayer Quantum Hall Systems at Filling Factor \nu=2: An Exact Diagonalisation Study

TL;DR

This study uses exact diagonalisation to analyze bilayer quantum Hall systems at filling factor two, confirming some mean-field predictions while revealing limitations in stability estimates at weak Zeeman coupling.

Contribution

It provides an exact numerical analysis of the phase boundary and stability of the canted antiferromagnetic phase, refining previous mean-field results.

Findings

Confirmed the phase boundary matches Hartree-Fock predictions.

Showed the state's stability at weak Zeeman coupling is overestimated by mean-field.

Identified degeneracies due to spin-rotation invariance in the absence of tunneling.

Abstract

We present an exact diagonalisation study of bilayer quantum Hall systems at a filling factor of two in the spherical geometry. We find the high-Zeeman-coupling phase boundary of the broken symmetry canted antiferromagnet is given exactly by previous Hartree-Fock mean-field theories, but that the state's stability at weak Zeeman coupling has been qualitatively overestimated. In the absence of interlayer tunneling, degeneracies occur between total spin multiplets due to the Hamiltonian's invariance under independent spin-rotations in top and bottom two-dimensional electron layers.