  We show that there is pseudospin SU(2) symmetry in the one-dimensional
tight-binding model with the inter-molecular electron-phonon interaction. We
discuss the relation between the pseudospin symmetry breaking and the
charge-density wave (CDW). For a finite lattice at half-filling, the Peierls
instability drives the lattice to {\it dimerization} at low temperature,
however, the system remains the SU(2) symmetry invariant and is not CDW state.
An attractive on-site electron-electron interaction makes the pseudospin
symmetry spontaneously broken in the thermodynamic limit and the CDW state
arises as well. Hence, it is clear that spontaneous pseudospin symmetry
breaking produces the CDW state.s the pseudospin symmetry spontaneously broken
in the thermodynamic limit and the CDW state arises as well. Hence, it is clear
that spontaneous pseudospin symmetry breaking produces the CDW state.
