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arXiv:quant-ph/0610055 · Physical Review A

Entanglement localization by a single defect in a spin chain

Tony J. G. Apollaro, Francesco Plastina

Published Dec 22, 2006• 38 citations
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Abstract

We discuss the effect of a single diagonal defect on both the static and dynamical properties of entanglement in a spin chain. We show that entanglement localizes at the defect and discuss its localization length, arguing that this can be used as a means to store entanglement. We also show that the impurity site can behave as an entanglement mirror and characterize the bouncing process in terms of reflection and transmission coefficients.

DOI
10.1103/physreva.74.062316

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We discuss the effect of a single diagonal defect on both the static and dynamical properties of entanglement in a spin chain. We show that entanglement localizes at the defect and discuss its localization length, arguing that this can be used as a means to store entanglement. We also show that the impurity site can behave as an entanglement mirror and characterize the bouncing process in terms of reflection and transmission coefficients.
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We investigate on how to generate maximally entangled states in systems characterized by the Hamiltonian of the XXZ\mathrm{XXZ}XXZ model with defects. Some proposed quantum computers are described by such a model. Defects embedded in this otherwise homogeneous spin chain are used to obtain Einstein-Podolsky-Rosen and W states. It is well known that a large defect localizes an excitation on the defect site. We can then consider a few identical and large defects to create a subsystem whose eigenstates are entangled. Here, we examine the cases of one and two excitations.
We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain - even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.