Adiabatic Construction of Hierarchical Quantum Hall States

Intuitive arguments and numerical simulations have long been used to argue for the incompressibility of fractionally quantized Hall states at the most prominent odd-denominator Landau-level filling fractions $\ensuremath{\nu}$ = $p$/($p$ ($m$ - 1) + 1), where $p$ is an integer and $m$ an odd integer. Here, the authors strengthen the case by deriving these states more rigorously via adiabatic localization of magnetic flux onto the particles. They arrive at wave functions suggested by Jain's composite-fermion picture.