Entanglement and Density Matrix of a Block of Spins in AKLT Model
Abstract
We study a 1dimensional 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 ValenceBondSolid (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 nonzero 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}.
 Publication:

Journal of Statistical Physics
 Pub Date:
 October 2008
 DOI:
 10.1007/s1095500896179
 arXiv:
 arXiv:0802.3221
 Bibcode:
 2008JSP...133..347X
 Keywords:

 AKLT;
 Density matrix;
 Entanglement;
 Valence Bond Solid;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Revised version, typos corrected, references added, 31 pages