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

We analyze transitions between quantum Hall ground states at prominent filling factors $\ensuremath{\nu}$ 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 wave functions (Laughlin, Moore-Read, Read-Rezayi). This scenario is shared by both odd $(\ensuremath{\nu}=1/3,1/5,3/5,7/3,11/5,13/5)$ and even denominator states $(\ensuremath{\nu}=1/2,1/4,5/2,9/4)$. In particular, the Fermi-liquid-like state at $\ensuremath{\nu}=1/2$ 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.