Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties such as the Moore-Read Pfaffian for filling factor $\nu =5/2$. This wavefunction has been constructed by constructing correlation functions of a two-dimensional conformal field theory (CFT) involving a free boson and a Majorana fermion. By considering other CFTs many other clustered states have been proposed as candidate fractional quantum Hall states under appropriate circumstances. It is believed that the underlying CFT should be unitary if one wants to describe an incompressible, i.e., gapped liquid state. We show that by changing the way one derives the wavefunction from its parent CFT it is possible to obtain an incompressible candidate state when starting from a nonunitary parent. The construction mimics a global change in parameters in the phase space of the electron system. We explicit our construction in the case of the so-called Gaffnian state (a state for filling factor 2/5) and also for the Haldane-Rezayi state (a spin-singlet state at filling 1/2). We note that there are obstructions along this path in the case of the permanent spin-singlet state of Read and Rezayi which can be characterized as a robust gapless state.

• Received 17 February 2009

DOI:https://doi.org/10.1103/PhysRevB.80.155324