Non-Abelian order with Landau-level mixing at filling 3/2

Which quantum Hall phase is favored by fully spin-polarized two-dimensional Coulomb electrons at filling ν=3/2 when Landau-level mixing is included? The problem is to distinguish competing orders, including Pfaffian and anti-Pfaffian candidates, beyond models projected onto a fixed set of Landau levels.

Why it matters and what counts as progress

Why it matters: Identifying the order clarifies whether this interacting-electron model supports an Ising-type non-Abelian phase and how mixing changes the competition between candidate states.

What counts as progress: Obtain better controlled energies, degeneracy, entanglement or overlap diagnostics, and establish how they scale with system size and mixing strength. Finite variational Monte Carlo evidence retains approximation and finite-size uncertainty; it does not prove a thermodynamic phase or settle the experimental ν=5/2 state.

How the problem developed

24 Jul 2024 · Experimental result [1]
Yiwei Chen and coauthors Reported even-denominator fractional quantum Hall states at ν = 3/2 in trilayer graphene and examined how tunable Landau-level mixing affected the observed states.
13 Oct 2026 · Numerical result [2]
Pierre-Antoine Graham, Ahmed Abouelkomsan and Liang Fu Reported an all-electron, all-Landau-level calculation at spin-polarized ν = 3/2; their neural-network variational wave function identifies Ising-type non-Abelian order and favors the anti-Pfaffian under Landau-level mixing.

AI contribution

Non-Abelian quantum Hall states at strong Landau level mixing: finding anyons with first-principles AI

Pierre-Antoine Graham, Ahmed Abouelkomsan, Liang Fu

Graham, Abouelkomsan and Fu report neural-network variational Monte Carlo evidence for Ising-type non-Abelian order in fully spin-polarized two-dimensional Coulomb electrons at filling ν=3/2, including Landau-level mixing. Ground-state degeneracies, entanglement and trial-state overlaps favor an anti-Pfaffian phase in the studied liquid regime.

AI involvementAI-centered

ImportanceNotable

Technical verificationPartial

Human understandingFull