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We analyze the effect of exchanging quasiholes described by Gaffnian quantumHall trial state wave functions. This exchange is carried out via adiabatictransport using the recently developed coherent state Ansatz. We argue that ourAnsatz is justified if the Gaffnian parent Hamiltonian has a charge gap, eventhough it is gapless to neutral excitations, and may therefore properlydescribe the adiabatic transport of Gaffnian quasiholes. For nonunitary statessuch as the Gaffnian, the result of adiabatic transport cannot agree with themonodromies of the conformal block wave functions, and may or may not lead towell-defined anyon statistics. Using the coherent state Ansatz, we find twounitary solutions for the statistics, one of which agrees with the statisticsof the non-Abelian spin-singlet state by Ardonne and Schoutens.

Gaffnian holonomy through the coherent state method