Entanglement and Density Matrix of a Block of Spins in AKLT Model

Ying Xu, Hosho Katsura, Takaaki Hirano, Vladimir E. Korepin

Published 2008-02-21, updated 2008-04-04Version 2

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.