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Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry

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.