In this work, quantum phase transitions in the one-dimensional Axial
Next-Nearest Neighbor Ising (ANNNI) model with transverse field were
investigated, with emphasis on the role of bipartite entanglement as a critical
indicator. The sensitivity of von Neumann entropy to phase changes was
analyzed, and how different choices of bipartitions influence its response in the
transition was evaluated.
Due to the absence of an exact solution for the model with transverse field at
the thermodynamic limit, we applied the Lanczos method to numerically
determine the ground state of finite chains with periodic boundary conditions.
The quantum critical points were estimated using finite-size scaling (FSS)
techniques. In addition, spin correlation functions and the structure factor were
calculated, allowing us to identify magnetic ordering and frustration effects,
including patterns associated with the devil's staircase. The results reinforce
that von Neumann entropy, in addition to adequately identifying the transition
between commensurate phases, is sensitive to spatial modulations originating
from the competition between interactions in the model.