We compute exactly the von Neumann entanglement entropy of the
eta-pairing states - a large set of exact excited eigenstates of the
Hubbard Hamiltonian. For the singlet eta-pairing states the entropy
scales with the logarithm of the spatial dimension of the (smaller)
partition. For the eta-pairing states with finite spin magnetization
density, the leading term can scale as the volume or as the
area-times-log, depending on the momentum space occupation of the
Fermions with flipped spins. We also compute the corrections to the
leading scaling. In order to study the eigenstate thermalization
hypothesis (ETH), we also compute the entanglement Rényi entropies of
such states and compare them with the corresponding entropies of thermal
density matrix in various ensembles. Such states, which we find violate
strong ETH, may provide a useful platform for a detailed study of the
time-dependence of the onset of thermalization due to perturbations
which violate the total pseudospin conservation.
Hubbard Hamiltonian in the dimer representation Large-U case
