  We propose an eigen-operator scheme to study the lattice model of interacting
spinless fermions at half filling and show that this model possesses a hidden
form of reflection positivity in its Majorana fermion representation. Based on
this observation, we prove rigourously that the ground state of this model is
either unique or doubly degenerate if the lattice size $N$ is even, and is
always doubly degenerate if $N$ is odd. This proof holds in all dimensions with
arbitrary lattice structures.

Strongly Correlated Electrons