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We exactly calculate the reduced density matrix of matrix product states(MPS). Our compact result enables one to perform analytic studies ofentanglement in MPS. In particular, we consider the MPS ground states of twoanisotropic spin chains. One is a q-deformed Affleck-Kennedy-Lieb-Tasaki (AKLT)model and the other is a general spin-1 quantum antiferromagnet withnearest-neighbor interactions. Our analysis shows how anisotropy affectsentanglement on different continuous parameter manifolds. We also construct aneffective boundary spin model that describes a block of spins in the groundstate of the q-deformed AKLT Hamiltonian. The temperature of this effectivemodel is given in terms of the deformation parameter q.

Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states