  We study the ground-state entanglement Hamiltonian of several disjoint
intervals for the massless Dirac fermion on the half-line. Its structure
consists of a local part and a bi-local term that couples each point to another
one in each other interval. The bi-local operator can be either diagonal or
mixed in the fermionic chiralities and it is sensitive to the boundary
conditions. The knowledge of such entanglement Hamiltonian is the starting
point to evaluate the negativity Hamiltonian, i.e. the logarithm of the
partially transposed reduced density matrix, which is an operatorial
characterisation of entanglement of subsystems in a mixed states. We find that
the negativity Hamiltonian inherits the structure of the corresponding
entanglement Hamiltonian. We finally show how the continuum expressions for
both these operators can be recovered from exact numerical computations in
free-fermion chains.
