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

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).

15 pages, published version, improved redaction

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Fractional Quantum Hall States and Jack Polynomials
• Topological Entanglement and Clustering of Jain Hierarchy States
• A nu=2/5 Paired Wavefunction
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Ordered structures in rotating ultracold Bose gases
• Halperin (m, m',n) bilayer quantum Hall states on thin cylinders
• Composite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields
• Testing the topological nature of the fractional quantum Hall edge
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
• Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions

Cited by in corpus (11)

• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• The structure of spinful quantum Hall states: a squeezing perspective
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Development of Grid e-Infrastructure in South-Eastern Europe
• Solvable models for unitary and non-unitary topological phases
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Gaplessness of the Gaffnian
• From the Gaffnian critical point to the incompressible 2/5 quantum Hall state