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We study the phase diagram of spinless fermions with nearest andnext-nearest-neighbor interactions in one dimension utilizing the (finite-size)density-matrix renormalization group (DMRG) method. The competition betweennearest and next-nearest-neighbor interactions and nearest-neighbor hoppinggenerates four phases in this model: two charge-density-wave insulators, aLuttinger liquid phase, and a bond-order phase. We use finite-size scaling ofthe gap and various structure factors to determine the phase diagram.

Phase diagram of the half-filled one-dimensional t-V-V' model