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

TL;DR

This paper investigates how tuning the interaction potential in quantum Hall systems induces phase transitions between compressible and incompressible states, revealing a first-order transition and the emergence of model wavefunctions like Moore-Read.

Contribution

It demonstrates that varying the interaction width causes compressible states to undergo first-order transitions to incompressible states, including the Moore-Read Pfaffian, in quantum Hall systems.

Findings

Compressible states transition to incompressible states with tuning.

Incompressible states are well described by model wavefunctions.

The Moore-Read Pfaffian emerges at large interaction widths.

Abstract

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