Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

► We adapt the infinite time-evolving block decimation algorithm. ► The one-dimensional two-body and three-body interactions spin model is investigate. ► The bifurcation of the ground-state fidelity per site for the model is unveiled. ► Local order parameters were derived for the model to characterize different phases.