  We investigate the nature of the quantum phase transition out of
charge-density-wave phase in the spinless fermion model with nearest- and
next-nearest-neighbor interaction at one-third filling. Using an extensive
Density Matrix Renormalization Group (DMRG) simulations we show that the
transition changes it nature. We show that for weak next-nearest-neighbor
coupling the transition is of Kosterlitz-Thouless type in agreement with
bosonisation predictions. We also provide strong numerical evidences that for
large next-nearest-neighbor repulsion the transition belongs to the
Pokrovsky-Talapov univerality class describing a non-conformal
commensurate-incommensurate transition. Finally, we argue that the change of
the nature of the transition is a result of incommensurability induced by
frustration and realized even at zero doping. The implications in the context
of XXZ chain with next-nearest-neighbor Ising interaction is briefly discussed.
