The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect

Abstract

We motivate a close look on the usefulness of the Gaffnian and Haffnian quasihole manifold (null spaces of the respective model Hamiltonians) for well-known gapped fractional quantum Hall (FQH) phases. The conformal invariance of these subspaces are derived explicitly from microscopic many-body states. The resultant CFT description leads to an intriguing emergent primary field with $h=2,c=0$, and we argue the quasihole manifolds are quantum mechanically well-defined and well-behaved. Focusing on the incompressible phases at $\nu =1/3$ and $\nu =2/5$, we show the low-lying excitations of the Laughlin phase are quantum fluids of Gaffnian and Haffnian quasiholes, and give a microscopic argument showing that the Haffnian model Hamiltonian is gapless against Laughlin quasielectrons. We discuss the thermal Hall conductance and shot noise measurements at $\nu =2/5$, and argue that the experimental observations can be understood from the dynamics within the Gaffnian quasihole manifold. A number of detailed predictions on these experimental measurements are proposed, and we discuss their relationships to the conventional CFT arguments and the composite fermion descriptions.

arXiv comment17+ pages, 6 figures, comments very welcome

References in corpus (46)

• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Fractional Quantum Hall States and Jack Polynomials
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Quantum Hall Physics - hierarchies and CFT techniques
• Observed Quantization of Anyonic Heat Flow
• Edge excitations of paired fractional quantum Hall states
• Bulk-Edge Correspondence in the Entanglement Spectra
• Topological Entanglement and Clustering of Jain Hierarchy States
• A nu=2/5 Paired Wavefunction
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• Evidence for a fractional quantum Hall state with anisotropic longitudinal transport
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Field theory of the quantum Hall nematic transition
• Scattering of Bunched Fractionally Charged Quasiparticles
• Conformal invariance of chiral edge theories
• Generalized Quantum Hall Projection Hamiltonians
• Topological Quantum Computing with Read-Rezayi States
• Composite fermion wave functions as conformal field theory correlators
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Conformal Field Theory of Composite Fermions
• Galois Conjugates of Topological Phases
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Microscopic theory for nematic fractional quantum Hall effect
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Collective excitations at filling factor 5/2: The view from superspace
• Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall Fluids
• Analytic Wavefunctions for Neutral Bulk Excitations in Fractional Quantum Hall Fluids
• Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Gaplessness of the Gaffnian
• Anomalous Nematic States in High Half-Filled Landau Levels
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory

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• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• From the Gaffnian critical point to the incompressible 2/5 quantum Hall state