Explicit monodromy of Moore-Read wave functions on a torus

TL;DR

This paper constructs explicit wave functions for the Moore-Read state on a torus with quasiholes, enabling the calculation of monodromy matrices that reveal how quasihole braiding affects ground state degeneracy and fusion channels.

Contribution

It provides explicit wave functions for the Moore-Read state with quasiholes on a torus and computes the monodromy matrix, explaining forbidden transitions via conformal field theory.

Findings

Monodromy matrix matches recent theoretical predictions

Quasihole braiding can change fusion channels and ground state parity

Certain ground state transitions are forbidden due to fusion channel constraints

Abstract

We construct the wave functions for the Moore-Read $\nu = 5/2$ quantum Hall state on a torus in the presence of two quasiholes. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. The result agrees with the recent discussion by Oshikawa {\it et al.} Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in some of the ground states.