Anyon exciton revisited: Exact solutions for a few-particle system
D. G. W. Parfitt, M. E. Portnoi
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.
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