  In past work we introduced a method which allows for exact computations of
entanglement Hamiltonians. The method relies on computing the resolvent for the
projected (on the entangling region) Green's function using a solution to the
Riemann-Hilbert problem combined with finite rank perturbation theory. Here we
analyze in detail several examples involving excited states of chiral fermions
(Dirac and Majorana) on a spatial circle. We compute the exact entanglement
Hamiltonians and an exact formula for the change in entanglement entropy due to
the introduction of a particle above the Dirac sea. For Dirac fermions, we give
the first-order temperature correction to the entanglement entropy in the case
of a multiple interval entangling region.
