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

TL;DR

This paper investigates the Gaffnian and Haffnian quasihole manifolds in fractional quantum Hall phases, deriving their conformal field theory descriptions, analyzing their physical relevance, and connecting theoretical predictions with experimental observations.

Contribution

It provides a microscopic derivation of the CFT description for Gaffnian and Haffnian quasiholes and explores their role in incompressible FQH phases, including experimental implications.

Findings

Gaffnian and Haffnian quasihole manifolds are well-defined and behave quantum mechanically.

Haffnian model Hamiltonian is gapless against Laughlin quasielectrons.

Experimental signatures at ν=2/5 can be explained by Gaffnian quasihole dynamics.

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.