Two leg quantum Ising ladder: A bosonization study of the ANNNI model

The quantum ANNNI chain in a transverse field is investigated by means of the bosonization approach in the limit of large next-nearest neighbor interaction. In this regime, this model can be viewed as a weakly coupled two-leg zigzag ladder which enables us to derive its low energy effective field theory. In particular, it is shown that the effect of frustration in the system is captured by the presence of a non zero conformal spin perturbation that accounts for the existence of all the incommensurate phases of the model.