  An interacting pair of polyacetylene chains are initially modeled as a couple
of undimerized polymers described by a Hamiltonian based on the tight-binding
model representing the electronic behavior along the linear chain, plus a
Dirac's potential double well representing the interaction between the chains.
A theoretical field formalism is employed, and we find that the system exhibits
a gap in its energy band due to the presence of a mass-matrix term in the
Dirac's Lagrangian that describes the system. The Peierls instability is
introduced in the chains by coupling a scalar field to the fermions of the
theory via spontaneous symmetry breaking, to obtain a kink-like soliton, which
separates two vacuum regions, i.e., two spacial configurations (enantiomers) of
the each molecule. Since that mass-matrix and the pseudo-spin operator do not
commute in the same quantum representation, we demonstrate that there is a
particle oscillation phenomenon with a periodicity equivalent to the Bloch
oscillations.
