Spinless fermion t-V chain ($H=-t{\sum }_j(c_{j+1}^{†}{c}_j+h.c.)+V{\sum }_j{n}_j{n}_{j+1}$)

A tight binding chain of one species of fermions with nearest-neighbour hopping and density interaction. At half filling and $V/|t|\to +\infty$, minimizing the interaction requires alternating occupied and empty sites. An even periodic chain has two such configurations at $t=0$; finite hopping admixes defects through virtual hopping. A finite ring can select superpositions rather than one ordered product state. Two uncoupled copies have four limiting ordered choices when each is half filled, without a general claim of exact finite-hopping fourfold state degeneracy.