From Kosterlitz-Thouless to Pokrovsky-Talapov transitions in spinless fermions and spin chains with next-nearest-neighbor interactions

We investigate the nature of the quantum phase transition out of density-wave phase in a spinless fermion model with nearest-and next-nearest-neighbor interaction at one-Third filling. Using extensive density matrix renormalization group (DMRG) simulations, we show that the transition changes it nature. For weak next-nearest-neighbor coupling the transition is of Kosterlitz-Thouless type, in agreement with bosonisation predictions. For large next-nearest-neighbor repulsion we provide numerical evidences that the transition belongs to the Pokrovsky-Talapov univerality class describing a nonconformal commensurate-incommensurate transition. 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 the XXZ chain with next-nearest-neighbor Ising interaction is briefly discussed.