A two-leg quantum Ising ladder: a bosonization study of the ANNNI model

The quantum axial next-to-nearest neighbour Ising (ANNNI) chain in a transverse field is investigated by means of the bosonization approach in the limit of the large next-to-nearest neighbour 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.