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 states at filling fractions $\nu =p\mathrm{/}(p(m-1)+1)$ with $m$ odd, from integer Hall states at $\nu =p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.