Entanglement in a Valence-Bond-Solid State

Abstract

We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem (continuous block of spins). It quantifies the entanglement of this block with the rest of the ground state. We prove that the entanglement approaches a constant value exponentially fast as the size of the subsystem increases. Actually we proved that the density matrix of the continuous block of spins depends only on the length of the block, but not on the total size of the chain [distance to the ends also not essential]. We also study reduced density matrices of two spins both in the bulk and on the boundary. We evaluated concurrencies.

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