Block Spin Density Matrix of the Inhomogeneous AKLT Model

TL;DR

This paper analyzes the density matrix of a block of spins in an inhomogeneous AKLT chain, revealing its structure and entropy properties, and demonstrating the behavior of the ground state in this generalized model.

Contribution

It extends the AKLT model to inhomogeneous cases and explicitly calculates the block density matrix and entropy, showing its projector form and saturation behavior.

Findings

Density matrix is a projector onto a subspace.

For large blocks, the density matrix approaches the identity in the subspace.

Von Neumann entropy saturates and equals Renyi entropy.

Abstract

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.