  We consider the algebra of massive fermions restricted to a diamond in
two-dimensional Minkowski spacetime, and in the Minkowski vacuum state. While
the massless modular Hamiltonian is known for this setting, the derivation of
the massive one is an open problem. We compute the small-mass corrections to
the modular Hamiltonian in a perturbative approach, finding some terms which
were previously overlooked. Our approach can in principle be extended to all
orders in the mass, even though it becomes computationally challenging.
