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.

17+ pages, 6 figures, comments very welcome

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Cited by in corpus (9)

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• 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