Adiabatic construction of hierarchical quantum Hall states

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall at filling fractions $\nu=p/(p(m-1)+1)$ with $m$ odd, from integer $\nu=p$ through adiabatic localization magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during process. The construction hence establishes existence incompressible these fillings.