  This paper revisits standard calculations of free field entanglement entropy
in light of the newly developed lattice-continuum correspondence. This
correspondence prescribes an explicit method to extract an approximately
continuum quantum field theory out of a fully regularized lattice theory. This
prescription will here be extended to subregion algebras, and it will be shown
how entropies of continuum boson and fermion theories can be computed by
working purely with lattice quantities. This gives a clear picture of the
origin of divergences in entanglement entropy while also presenting a concise
and detailed recipe for calculating this important quantity in continuum
theories.
