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A relation between entanglement and criticality of spin chains isestablished. The entanglement we exploit is shared between auxiliary particles,which are isolated from each other, but are coupled to the same criticalspin-1/2 chain. We analytically evaluate the reduced density matrix, andnumerically show the entanglement of the auxiliary particles in the proximityof the critical points of the spin chain. We find that the entanglement inducedby the spin-chain may reach one, and it can signal very well the criticalpoints of the chain. A physical understanding and experimental realization withtrapped ions are presented.Comment: 5 pages, 4figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Entanglement induced in spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>particles by a spin chain near its critical points

Entanglement induced in spin-1∕2particles by a spin chain near its critical points