Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions

TL;DR

This paper investigates neutral collective modes in fractional quantum Hall states, especially the anti-Pfaffian state, using parton theory to test supersymmetry conjectures and compute excitation dispersions.

Contribution

It constructs explicit wave functions for neutral excitations in the anti-Pfaffian state and evaluates their properties for large systems, extending the understanding of neutral modes in quantum Hall states.

Findings

Long-wavelength gaps of neutral modes are close for the anti-Pfaffian state.

Computed dispersions of various neutral excitations including magnetoroton and neutral fermion.

Proposed a parton-exciton model for neutral excitations in the composite Fermi liquid.

Abstract

The Moore-Read Pfaffian (Pf) state exhibits two distinct neutral excitation modes, the bosonic magnetoroton mode, and the neutral fermion mode. These two modes have been conjectured to be supersymmetric (SUSY) partners in the long-wavelength limit. Previous studies on these neutral excitations of the Pf state have shown evidence in favor of SUSY in the vicinity of the second Landau level (SLL) Coulomb interaction. Inspired by that, using the framework of parton theory, we test the SUSY conjecture for a state that lies in the same universality class as the particle-hole conjugate of the Pf, namely the anti-Pf (aPf) state, by constructing explicit wave functions for its magnetoroton and neutral fermion excitations and evaluating them for very large system sizes. As with the previous studies on the Pf state, we find that the long-wavelength gaps of the neutral modes of the parton state belonging to the same topological class as the aPf are close to each other for the SLL Coulomb interaction. Furthermore, using the parton wave functions, we compute the dispersion of various neutral collective excitations, including the magnetoroton, neutral fermion, and parton-excitons, for several notable non-Abelian and Abelian states. Finally, we propose a parton-exciton ansatz for the gapped neutral excitation of the composite fermion Fermi liquid at quarter filling and compute its dispersion for the Coulomb interaction in the lowest Landau level.