Entanglement and SU(n) symmetry in one-dimensional valence-bond solid states

Here we evaluate the many-body entanglement properties of a generalized SU(n) valence-bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for an elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and Renyi entropies of a block, localizable entanglement, and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU(2) case.