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In this paper we give an exact infinite-series expression for the bi-partiteentanglement entropy of the quantum Ising model both with a boundary magneticfield and in infinite volume. This generalizes and extends previous resultsinvolving the present authors for the bi-partite entanglement entropy ofintegrable quantum field theories, which exploited the generalization of theform factor program to branch-point twist fields. In the boundary case, weisolate in a universal way the part of the entanglement entropy which isrelated to the boundary entropy introduced by Affleck and Ludwig, and explainhow this relation should hold in more general QFT models. We provide severalconsistency checks for the validity of our form factor results, notably, theidentification of the leading ultraviolet behaviour both of the entanglemententropy and of the two-point function of twist fields in the bulk theory, to agreat degree of precision by including up to 500 form factor contributions.

Bi-partite entanglement entropy in massive QFT with a boundary: the Ising model