  Quantum state, in relativistic quantum mechanics, itself turns out to be an
entangled state due to its own degrees freedom such as spin and momentum. This
peculiar entanglement leaves the transformed state mixed. We consider the
fractional charge state that arises in a theory of fermion interacting with
scalar background in this context. The apparent entanglement occurs between
fermion ans scalar through Yukawa-type interaction. However, the spontaneous
symmetry breaking causes appearance of the $c$-number zero energy solution of
the Dirac equation as a pure state. Quantum entanglement in such relativistic
system is proposed to have a microscopic view of the spontaneous symmetry
breaking which has been realised in condensed matter system like polyacetylene.
