Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

TL;DR

This paper investigates the Pfaffian model for the nu=5/2 fractional quantum Hall effect through numerical analysis, comparing it with exact results and discussing its implications for quasihole excitations and nonabelian statistics.

Contribution

It provides a detailed numerical study of the Pfaffian model's accuracy and limitations for the nu=5/2 FQHE, including spectrum structure and symmetry considerations.

Findings

The Pfaffian model captures key features of quasihole excitations.

Discrepancies in degeneracy splittings highlight limitations.

Discussion on alternative explanations for the 5/2 FQHE state.

Abstract

The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at nu=5/2. 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.