  We study the entanglement spectrum of spin-1/2 XXZ ladders both analytically
and numerically. Our analytical approach is based on perturbation theory
starting either from the limit of strong rung coupling, or from the opposite
case of dominant coupling along the legs. In the former case we find to leading
order that the entanglement Hamiltonian is also of nearest-neighbor XXZ form
although with an in general renormalized anisotropy. For the cases of XX and
isotropic Heisenberg ladders no such renormalization takes place. In the
Heisenberg case the second order correction to the entanglement Hamiltonian
consists of a renormalization of the nearest neighbor coupling plus an
unfrustrated next nearest neighbor coupling. In the opposite regime of strong
coupling along the legs, we point out an interesting connection of the
entanglement spectrum to the Lehmann representation of single chain spectral
functions of operators appearing in the physical Hamiltonian coupling the two
chains.
