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 (DMRG) 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. 
Tapan Mishra, Juan Carrasquilla, Marcos Rigol
cond-mat.str-el cond-mat.quant-gas