Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems

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We analyze transitions between quantum Hall ground states at prominent filling factors ν in the spherical geometry by tuning the width parameter of the Zhang-Das Sarma interaction potential. We find that incompressible ground states evolve adiabatically under this tuning, whereas the compressible ones are driven through a first order phase transition. Overlap calculations show that the resulting phase is increasingly well described by appropriate analytic model wavefunctions (Laughlin, Moore-Read, Read-Rezayi). This scenario is shared by both odd (ν=1/3, 1/5, 3/5, 7/3, 11/5, 13/5) and even denominator states (ν=1/2, 1/4, 5/2, 9/4). In particular, the Fermi liquid-like state at ν=1/2 gives way, at large enough value of the width parameter, to an incompressible state identified as the Moore-Read Pfaffian on the basis of its entanglement spectrum.