Entanglement Entropy in 1-D integrable chains

We study analytically the Renyi entropy of a bipartite lattice in the limit of two semi-infinite chains joined at the origin, for a few integrable 1-dimensional models, by using the techniques of Corner Transfer Matrices of the corresponding 2-D classical systems, namely the 8-vertex model and the RSOS. In the scaling limit, close to a conformal point, we reproduce the leading behavior expected from CFT prediction. The sub-leading corrections, however, differ from na\"ive expectations and we show that lattice effect can give rise to additional relevant terms in any numerical approach. Moreover, in the vicinity of a non-conformal (ferromagnetic) point, we observe a violation of universality and a behavior of the entropy characteristic of an {\it essential singularity}.