Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect

TL;DR

This paper demonstrates that in a fractional quantum Hall system, the character of quasiholes can change nonperturbatively without the energy gap closing, indicating a more complex evolution of excitations than previously assumed.

Contribution

It reveals that quasiholes in the ν=2/5 fractional quantum Hall state change character nonperturbatively when transitioning from a Gaffnian to Coulomb interaction, challenging the invariance assumption.

Findings

Quasiholes change character nonperturbatively during interaction transition.

States below the gap correspond to composite fermion theory.

Gaffnian quasiholes are unstable to composite fermion formation.

Abstract

It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian during which the gap does not close. We show in this article that, at least for finite systems, as the interaction is changed from a model three body interaction to Coulomb, the ground state at filling factor $\nu=2/5$ evolves continuously from the so-called Gaffnian wave function to the composite fermion wave function, but the quasiholes alter their character in a nonperturbative manner. This is attributed to the fact that the Coulomb interaction opens a gap in the Gaffnian quasihole sector, pushing many of the states to very high energies. Interestingly, the states below the gap are found to have a one-to-one correspondence with the composite fermion theory, suggesting that the Gaffnian model contains composite fermions, and that the Gaffnian quasiholes are unstable to the formation of composite fermions when a two-body interaction term is switched on. General implications of this study are discussed.