  A one-dimensional quantum spin model with the competing two-spin and
three-spin interactions is investigated in the context of a tensor network
algorithm based on the infinite matrix product state representation. The
algorithm is an adaptation of Vidal's infinite time-evolving block decimation
algorithm to a translation-invariant one-dimensional lattice spin system
involving three-spin interactions. The ground-state fidelity per lattice site
is computed, and its bifurcation is unveiled, for a few selected values of the
coupling constants. We succeed in identifying critical points and deriving
local order parameters to characterize different phases in the conventional
Ginzburg-Landau-Wilson paradigm.
