Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level

TL;DR

This paper generalizes quantum Hall states beyond the Pfaffian by introducing exact ground states with k+1-body interactions, revealing new nonabelian quasiparticles and connections to conformal field theory.

Contribution

It introduces a family of exactly solvable quantum Hall states involving k-particle clusters, extending the Pfaffian state to higher k and linking them to parafermion correlators.

Findings

Exact ground states for all k > 0 with k+1-body interactions.

Wavefunctions involve k-particle clusters and relate to parafermion conformal field theory.

Large overlaps with Coulomb ground states at specific filling factors for k=3.

Abstract

The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions, for all integers k > 0. The remarkably simple wavefunctions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The k=2 case is the Pfaffian. For k > 1, the quasiparticle excitations of these systems are expected to possess nonabelian statistics, like those of the Pfaffian. For k=3, these ground states have large overlaps with the ground states of the (2-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors \nu=2+3/5, 2+2/5.