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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 fidelityapproach. We numerically determined the fidelity susceptibility as a functionof the transverse field $B_x$ and the strength of the next-nearest-neighborinteraction $J_2$, for systems of up to 24 spins. We also examine theground-state vector with respect to the spatial ordering of the spins. Theground-state phase diagram shows ferromagnetic, paramagnetic, floating,$\Braket{2,2}$ phases, and we predict an infinite number of modulated phases inthe thermodynamic limit ($L \rightarrow \infty$). The transition linesseparating the modulated phases seem to be of second-order, whereas the linebetween the floating and the $\Braket{2,2}$ phases is possibly of first-order.

Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field