  Exploiting the entanglement concept within a matrix-product-state based
infinite density-matrix renormalization group approach, we show that the
spin-density-wave and bond-order-wave ground states of the one-dimensional
half-filled extended Hubbard model give way to a symmetry-protected topological
Haldane state in case an additional alternating ferromagnetic spin interaction
is added. In the Haldane insulator the lowest entanglement level features a
characteristic twofold degeneracy. Increasing the ratio between
nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the
entanglement entropy, the variation of the charge, spin and neutral gaps, and
the dynamical spin/density response signal a quantum phase transition to a
charge-ordered state. Below a critical point, which belongs to the universality
class of the tricritical Ising model with central charge 7/10, the model is
critical with $c=1/2$ along the transition line. Above this point, the
transition between the Haldane insulator and charge-density-wave phases becomes
first order.
