Investigation of trial wavefunction approach to bilayer Quantum Hall systems

TL;DR

This paper analyzes known trial wavefunctions in bilayer quantum Hall systems at total filling factor 1, revealing limitations in their ability to accurately describe excitations and highlighting the need for better trial wavefunctions.

Contribution

It demonstrates that existing trial wavefunctions like the quasi-hole and meron have significant shortcomings, emphasizing the challenge of finding accurate trial states for these systems.

Findings

Quasi-hole wavefunction's charge extends over the entire system.

Energy of meron increases logarithmically with separation.

Naive pair of meron wavefunction's energy increases quadratically with separation.

Abstract

We study properties of some known trial wavefunctions in bilayer quantum Hall systems at the total filling factor $ \nu_{T}=1 $. In particular, we find that the properties of a meron wavefunction and a natural "quasi-hole" wave function are dramatically different due to the broken symmetry and the associated Goldstone mode in the bulk. Although the (smallest) meron has localized charge $ 1/2 $ and logarithmically divergent energy, the charge of the quasi-hole excitation extends over the whole system and its energy diverges linearly with the area of the system. This indicates that the natural quasi-hole wavefunction is not a good trial wavefunction for excitations. It also shows that the energy of the naive candidate for a pair of meron wavefunction written down previously increases quadratically instead of logarithmically as their separation increases. Our results indicate that qualitatively good trial wave functions for the ground state and the excitations of the interlayer coherent bilayer quantum Hall system at finite $ d $ are still not available and searching for them remains an important open problem.