Determine the nature of the ν = 5/2 fractional quantum Hall state

Determine which topological order is realized in the ν = 5/2 fractional quantum Hall state in GaAs, whose nature remains unresolved among the Pfaffian, anti-Pfaffian, and particle–hole Pfaffian possibilities.

Background

The paper explains that the even-denominator ν = 5/2 fractional quantum Hall state was proposed to be the Moore–Read Pfaffian, but that the anti-Pfaffian and particle–hole Pfaffian are also viable candidate topological orders. Experimental thermal-transport results have been interpreted as supporting the particle–hole Pfaffian, whereas numerical studies have generally favored other possibilities.

The unresolved status of the ν = 5/2 state is distinct from the paper’s main result, which studies the fully spin-polarized ν = 3/2 state with strong Landau-level mixing and finds evidence favoring anti-Pfaffian order. The Discussion identifies ν = 5/2 as a natural extension because its Landau-level mixing also involves opposite-spin electrons.

References

This tension has motivated various proposals involving disorder and edge physics, and more than three decades after its discovery, the nature of the $\nu = 5/2$ state remains an open question.

— Non-Abelian quantum Hall states at strong Landau level mixing: finding anyons with first-principles AI  (2610.18967 - Graham et al., 13 Oct 2026) in Introduction