Trial wave function approach to bilayer quantum Hall systems

Abstract

We study the properties of some known trial wave functions in bilayer quantum Hall systems at the total filling factor ${\ensuremath{\nu}}_{T}=1$. In particular, we find that the properties of a meron wave function and a natural ``quasihole'' 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 quasihole excitation extends over the whole system and its energy diverges linearly with the area of the system. This indicates that the natural quasihole wave function is not a good trial wave function for excitations. It also shows that the energy of the naive candidate for a pair of meron wave functions 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.