The Valence-Bond-Solid (VBS) state was first introduced as the ground state of the celebrated Affleck-Kennedy-Lieb-Tasaki (AKLT) spin chain model in statistical mechanics. Then it became essential in condensed matter physics, quantum information and measurement-based quantum computation. Recent studies elucidated important entanglement properties of VBS states. We start with the definition of a general AKLT model and the construction of VBS ground states. In order to study entanglement, a block subsystem is introduced and described by the density matrix and the block Hamiltonian. Exact spectrum properties of the density matrix are proved and discussed. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and the Rényi entropy) are calculated. Both entropies take the saturated value and the density matrix is proportional to a projector in the large block limit.

Brief CV: Dr Ying Xu is now a postdoctoral fellow Institute for Theoretical Physics, University of Innsbruck, Austria, working with Prof. Hans Briegel. He received his BS degree from Fudan University, MS degree from The City College of The City University of New York, 2005, and Ph.D. from the State University of New York at Stony Brook in 2009. His research interests are Quantum Information and Computation, Statistical Mechanics, Condensed Matter Physics.