  In this paper we give an exact infinite-series expression for the bi-partite
entanglement entropy of the quantum Ising model both with a boundary magnetic
field and in infinite volume. This generalizes and extends previous results
involving the present authors for the bi-partite entanglement entropy of
integrable quantum field theories, which exploited the generalization of the
form factor program to branch-point twist fields. In the boundary case, we
isolate in a universal way the part of the entanglement entropy which is
related to the boundary entropy introduced by Affleck and Ludwig, and explain
how this relation should hold in more general QFT models. We provide several
consistency checks for the validity of our form factor results, notably, the
identification of the leading ultraviolet behaviour both of the entanglement
entropy and of the two-point function of twist fields in the bulk theory, to a
great degree of precision by including up to 500 form factor contributions.
