Analytic Wavefunctions for Collective Modes in Fractional Quantum Hall Fluids

TL;DR

This paper introduces simple analytic wavefunctions for neutral collective modes in fractional quantum Hall states, enabling new calculations and extending plasma analogy concepts to neutral excitations.

Contribution

It provides a novel analytic scheme for modeling collective modes in FQH states, including magneto-roton and neutral fermion modes, with applications to thermodynamic limit calculations.

Findings

Analytic wavefunctions for collective modes are derived.

Long wavelength neutral energy gap relates to charge fusion in plasma analogy.

A diagrammatic method for representing these wavefunctions is developed.

Abstract

We show model wavefunctions for neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" works for the magneto-roton modes of single-component Abelian and non-Abeliean FQH states, as well as neutral fermion mode for the Moore-Read (MR) state. The analytic wavefunctions enable computations in the thermodynamic limit previous inaccessible to numerics, and the long wavelength limit of the neutral energy gap of the magneto-roton modes can be interpreted as fusion of charges in two-dimensional plasma picture, extending the plasma analogy to neutral excitations. A lattice diagrammatic method of representing these many-body wavefunctions and FQH elementary excitations is also presented.