In this work we analyze the ground-state properties of the s=1/2
one-dimensional ANNNI model in a transverse field using the quantum fidelity
approach. We numerically determined the fidelity susceptibility as a function
of the transverse field Bx and the strength of the next-nearest-neighbor
interaction J2, for systems of up to 24 spins. We also examine the
ground-state vector with respect to the spatial ordering of the spins. The
ground-state phase diagram shows ferromagnetic, paramagnetic, floating,
⟨2,2⟩ phases, and we predict an infinite number of modulated phases in
the thermodynamic limit (L→∞). The transition lines
separating the modulated phases seem to be of second-order, whereas the line
between the floating and the ⟨2,2⟩ phases is possibly of first-order.Comment: 10 pages, 20 figure