  We consider free-fermion chains in the ground state and the entanglement
Hamiltonian for a subsystem consisting of two separated intervals. In this
case, one has a peculiar long-range hopping between the intervals in addition
to the well-known and dominant short-range hopping. We show how the continuum
expressions can be recovered from the lattice results for general filling and
arbitrary intervals. We also discuss the closely related case of a single
interval located at a certain distance from the end of a semi-infinite chain
and the continuum limit for this problem. Finally, we show that for the double
interval in the continuum a commuting operator exists which can be used to find
the eigenstates.
