Anyon exciton revisited: Exact solutions for a few-particle system

TL;DR

This paper extends the anyon exciton model to systems with multiple anyons, providing exact solutions and basis functions for such complex excitons, including interaction matrix elements and binding energies.

Contribution

It introduces a generalized model for neutral excitons with arbitrary anyon number, offering a complete basis and exact solutions for interaction energies.

Findings

Derived explicit interaction matrix elements for six-particle systems.

Obtained exact binding energies for excitons with zero momentum and angular momentum.

Classified exciton basis functions using partition theory.

Abstract

The anyon exciton model is generalized to the case of a neutral exciton consisting of a valence hole and an arbitrary number N of fractionally-charged quasielectrons (anyons). A complete set of exciton basis functions is obtained and these functions are classified using a result from the theory of partitions. Expressions are derived for the inter-particle interaction matrix elements of a six-particle system (N=5), which describes an exciton against the background of an incompressible quantum liquid with filling factor 2/5. Several exact results are obtained in a boson approximation, including the binding energy of a (N+1)-particle exciton with zero in-plane momentum and zero internal angular momentum.