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

TL;DR

This paper analyzes the density matrix of a block of spins in the AKLT model, revealing it as a projector with a specific subspace dimension and showing that the von Neumann entropy approaches a logarithmic value for large blocks.

Contribution

It provides a detailed characterization of the density matrix and entanglement entropy in the AKLT spin chain, highlighting the projector structure and entropy behavior.

Findings

Density matrix is a projector onto a (S+1)^2-dimensional subspace.

For large blocks, von Neumann entropy equals Renyi entropy.

Entanglement entropy approaches ln((S+1)^2) for large blocks.

Abstract

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