Entanglement in a Valence-Bond-Solid State

Details Entanglement in a Valence-Bond-Solid State Entanglement in a Valence-Bond-Solid State

2004-06-10

arxiv.org/abs/quant-ph/0406067v3

PRL, vol 93, issue 22, 227203, 2004

Physics

Quantum Physics

4pages, no figures

Scientific paper

10.1103/PhysRevLett.93.227203

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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