Abstract
We study a model (i.e., the ${t}_{2}\text{\ensuremath{-}}V$ model involving next-nearest-neighbor hopping and nearest-neighbor repulsion) in one dimension that generically depicts the dominant transport mechanism in cooperative strong electron-phonon interaction systems. Using analytic and numerical approaches, hard-core bosons are shown to typically undergo a striking discontinuous transition from a superfluid to a supersolid. Topological inequivalence of rings with even and odd number of sites is manifested through observable differences (in structure factor peaks) at the transition. Connections are also identified between the ${t}_{2}\text{\ensuremath{-}}V$ model and other topologically interesting models.
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