Disorder-driven transition and intermediate phase for $\nu=5/2$ fractional quantum Hall effect

TL;DR

This study investigates how disorder affects the $ u=5/2$ fractional quantum Hall state, revealing a disorder-driven phase transition, an intermediate phase possibly related to puddle states, and a transition to a composite Fermi liquid at high disorder.

Contribution

It provides the first unbiased numerical analysis of disorder effects on the $ u=5/2$ FQH state, identifying a phase transition and an intermediate phase with potential relevance to non-Abelian topological order.

Findings

Disorder induces a continuous phase transition in the $ u=5/2$ FQH state.

An intermediate phase, possibly a puddle state, emerges before the transition to a composite Fermi liquid.

In strong disorder, a composite Fermi liquid phase with fluctuating Chern numbers is observed.

Abstract

The fractional quantum Hall (FQH) effect at the filling number $\nu=5/2$ is a primary candidate for non-Abelian topological order, while the fate of such a state in the presence of random disorder has not been resolved. Here, we address this open question by implementing unbiased diagnosis based on numerical exact diagonalization. We calculate the disorder averaged Hall conductance and the associated statistical distribution of the topological invariant Chern number, which unambiguously characterize the disorder-driven collapse of the FQH state. As the disorder strength increases towards a critical value, a continuous phase transition is detected based on the disorder configuration averaged wave function fidelity and the entanglement entropy. In the strong disorder regime, we identify a composite Fermi liquid (CFL) phase with fluctuating Chern numbers, in striking contrast to the well-known $\nu=1/3$ case where an Anderson insulator appears. Interestingly, the lowest Landau level projected local density profile, the wavefunction overlap, and the entanglement entropy as a function of disorder strength simultaneously signal an intermediate phase, which may be relevant to the recent proposal of Pfaffian-anti-Pfaffian puddle state.