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

Understand

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.