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Title: Which topological order describes the $5/2$ quantum Hall state
Plain: Several candidate wavefunctions (named Pfaffian, anti-Pfaffian and particle-hole Pfaffian) predict different edge structures for the $5/2$ state, and experiments and computer simulations currently point to different answers.
Precise: For $\nu = 5/2$ in high-mobility GaAs quantum wells, determine the topological order. The thermal Hall conductance $\kappa_{xy} = c \kappa_0$, $\kappa_0 = \pi^2 k_B^2 T/(3h)$, distinguishes Pfaffian ($c = 7/2$), PH-Pfaffian ($c = 5/2$) and anti-Pfaffian ($c = 3/2$); the measured value is $5/2$ (Banerjee et al., 2018), while numerics with Landau-level mixing favour anti-Pfaffian or Pfaffian. An answer is an identification consistent with thermal Hall, upstream neutral modes, tunnelling exponents and numerics.
Settled by: Thermal Hall measurements with controlled edge equilibration, combined with numerics including realistic Landau-level mixing and disorder.
Kind: well-posed
Answer type: identification
References: (empty)
Literature status: contested
Status note: Experiments favour PH-Pfaffian (thermal Hall 2018; neutral-mode noise, Dutta et al. 2022; time-domain braiding noise consistent with PH-Pfaffian, arXiv:2608.12897, 2026), while numerics favour anti-Pfaffian or Pfaffian; proposed reconciliations (incomplete edge equilibration, domains, disorder-stabilized PH-Pfaffian) are debated as of 2026.
Posed since: (empty)