Numerical studies of the Pfaffian model of the ν=52 fractional quantum Hall effect

The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at ν=52. We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies and off-diagonal long-range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.