The problem of noninteracting singlet excitons (of the Frenkel variety) in a one-dimensional crystal is investigated using a second-quantization formalism. It is shown that only for the nearest-neighbor approximation in the open linear chain does the many-body solution result in independent quasiparticles exhibiting exact fermion behavior. The choice of coordinates for a general problem is briefly discussed and an expression is given which allows one to expand any (second-quantized) operator in terms of a set of either exact boson or fermion creation and annihilation operators.
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Chesnut et al. (1963) studied this question.
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