Charge-density-wave instabilities driven by multiple umklapp scattering

We show that the concept of umklapp-scattering driven instabilities in one-dimensional systems can be generalized to arbitrary multiple umklapp-scattering processes at commensurate fillings given that the system has sufficiently longer range interactions. To this end we study the fundamental model system, namely, interacting spinless fermions on a one-dimensional lattice, via a density-matrix renormalization-group approach. The instabilities are investigated via a method allowing to calculate the ground-state charge stiffness numerically exactly. The method can be used to determine other ground-state susceptibilities in general.