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

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

2008-02-21

arxiv.org/abs/0802.3221v2

Jour. Stat. Phys. vol 133, no. 2, 347-377 (2008)

Physics

Quantum Physics

Revised version, typos corrected, references added, 31 pages

Scientific paper

10.1007/s10955-008-9617-9

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 $\ln(S+1)^{2}$.

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