Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories

TL;DR

This paper introduces a modified Coulomb gas approach to construct quantum Hall states from non-unitary conformal field theories, enabling the creation of incompressible states like the Gaffnian and Haldane-Rezayi states.

Contribution

It demonstrates that changing the derivation method from a parent CFT allows for incompressible quantum Hall states from non-unitary theories, expanding the landscape of candidate states.

Findings

Constructed incompressible states from non-unitary CFTs.

Applied method to Gaffnian and Haldane-Rezayi states.

Showed phase space parameter change yields gapped states.

Abstract

Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties like 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 FQH 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 non-unitary parent. The construction mimics a global change of 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).