- Letter
From the Gaffnian critical point to the incompressible 2/5 quantum Hall state
Phys. Rev. B 105, L041305 – Published 31 January, 2022
DOI: https://doi.org/10.1103/PhysRevB.105.L041305
Abstract
Despite the high overlap with the exact Coulomb ground state, the so-called Gaffnian state fails to describe the incompressibility at the 2/5 quantum Hall filling factor and consequently it was conjectured to be a quantum critical state. To achieve a gapped state starting from the Gaffnian wave function, which we interpret as the interflavor pairing of the composite fermions, we propose a minimally “modified Gaffnian” wave function keeping the pairing intact. We find that a suitable hybridization of these two wave functions is an excellent description of the 2/5 quantum Hall state. It has a very high overlap with the exact Coulomb state and their entanglement spectra match up to reasonably higher levels. Interestingly, this hybridized wave function being a representative of a paired state suggests an exotic possibility of non-Abelian quasiparticle excitations at 2/5 filling.
