  We present a detailed study of the fidelity, the entanglement entropy, and
the entanglement spectrum, for a dimerized chain of spinless fermions---a
simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions
which is a well-known example for a model supporting a symmetry protected
topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is
tridiagonal and the eigenvalues and -vectors can be given explicitly as a
function of a single parameter which is known analytically for odd chain
lengths and can be determined numerically in the even length case. From a
scaling analysis of these data for essentially semi-infinite chains we obtain
the fidelity susceptibility and show that it contains a boundary contribution
which is different in the topologically ordered than in the topologically
trivial phase. For the entanglement spectrum and entropy we confirm predictions
from massive field theory for a block in the middle of an infinite chain but
also consider blocks containing the edge of the chain. For the latter case we
show that in the SPT phase additional entanglement---as compared to the trivial
phase---is present which is localized at the boundary. Finally, we extend our
study to the dimerized chain with a nearest-neighbour interaction using exact
diagonalization, Arnoldi, and density-matrix renormalization group methods and
show that a phase transition into a topologically trivial charge-density wave
phase occurs.
