Evidence for a floating phase of the transverse ANNNI model at high frustration

We study the transverse quantum ANNNI model in the region of high frustration (κ>0.5) using the density matrix renormalization group algorithm. We obtain a precise determination of the phase diagram, showing clear evidence for the existence of a floating phase, separated from the paramagnetic modulated phase by a high-order critical line ending at the multicritical point. We obtain simple and accurate formulas for the two critical lines.