Fermion Behavior of One-Dimensional Excitons

Abstract

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.