Ground state properties of the ANNNI model in a transverse field: A quantum fidelity approach

We analyze the ground-state properties of the {\$}s$=$1/2{\$} one-dimensional ANNNI model in a transverse field using the approach of quantum fidelity. We numerically determine the fidelity susceptibility as a function of the transverse field ({\$}B\textunderscore x{\$}) and the strength of the nearest-next-neighbor interaction ({\$}J\textunderscore 2{\$}) for systems of up to 24 spins. By analyzing the ground-state eigenvectors of finite systems, we expect that at the thermodynamic limit, the system will have an infinite number of phases, a ferromagnetic phase, a kink phase, an infinite number of modulated phases, floating phase and an antiphase.