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 $\nu =p/(p(m-1)+1)$ 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, as we explicitly show for the $p=2$ series of states. The construction hence provides a major step towards establishing the existence of incompressible states at these fillings.

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• Anyons
• Composite fermions
• Fractional quantum Hall effect
• Exact solutions for many-body systems