  We consider a general one-dimensional tight-binding electron model which has
a period $P$. For any filling factor $\nu$ such that $P\nu$ is non-integral, we
prove that the model in the infinite volume limit has either a symmetry
breaking or a unique ground state with gapless excitations. The proof is based
on the idea of Yamanaka, Oshikawa and Affleck (cond-mat/9701141), who extended
the Lieb-Schultz-Mattis argument to electron systems.
