Phase diagram of the half-filled one-dimensional t-V-V′ model

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