  We devise a method based on the tensor-network formalism to calculate genuine
multisite entanglement in ground states of infinite spin chains containing
spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing
an infinite time-evolving block decimation method acting upon an initial matrix
product state for the infinite spin system. We explicitly show how such
infinite matrix product states with translational invariance provide a natural
framework to derive the generalized geometric measure, a computable measure of
genuine multisite entanglement, in the thermodynamic limit of quantum many-body
systems with both spin-1/2 and higher-spin particles.
