  We study the 1D ferromagnetic Ising (spin-1/2) model with the
Dzyaloshinskii-Moriya (DM) interaction. We analyze the low energy excitation
spectrum and the ground state magnetic phase diagram using the Lanczos method.
The DM interaction-dependency is calculated for the low-energy excitation
spectrum, spiral order parameter and spin-spin correlation functions. We show
that a metamagnetic quantum phase transition occurs between the ferromagnetic
and spiral phases. The existence of the metamagnetic phase transition is
confirmed, using the variational matrix product states approach.
