The 16-fold Way and the Quantum Hall Effect at ν=5/2

Numerous topological orders were proposed in the QHE at the filling factor ν=5/2. We show that the popular Pfaffian, SU(2)₂, 113, K=8, 331, PH-Pfaffian orders, and their particle-hole conjugates can be classified in terms of Kitaev's 16-fold way. The experimental evidence for composite fermions at ν=5/2 suggests that only the topological orders of the 16-fold way are viable 5/2 states. We use a coupled QHE strip construction to generate Hamiltonians for all 16 orders from the parent Hamiltonians for the Pfaffian and K=8 states. We address the signatures of the 16 orders in Mach-Zehnder and Fabry-Pérot interferometry, and electrical and thermal transport. Only the PH-Pfaffian order is compatible with the existing data in GaAs at charge densities n∼3×10¹¹cm⁻².