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arXiv:quant-ph/0310177 · Physical Review A

Entanglement versus chaos in disordered spin chains

Léa Ferreira dos Santos, Gustavo Rigolin, Carlos O. Escobar

Published Apr 9, 2004• 97 citations
arXivHTMLPDF

Abstract

We use a Heisenberg spin-1∕2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized (localized) and in the chaotic (nonchaotic) regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a nonchaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbors) than for weakly interacting qubits (next and next-next neighbors).

DOI
10.1103/physreva.69.042304

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We use a Heisenberg spin-1∕2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized (localized) and in the chaotic (nonchaotic) regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a nonchaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbors) than for weakly interacting qubits (next and next-next neighbors).
We use a disordered antiferromagnetic spin-1∕21∕21∕2 chain with anisotropic exchange coupling to model an array of interacting qubits. All qubits have the same level spacing, except two, which are called the defects of the chain. The level spacings of the defects are equal and much larger than all the others. We investigate how the entanglement between the two defects depends on the anisotropy of the system. When the anisotropy coupling is much larger than the energy difference between a defect and an ordinary qubit, the two defects become strongly entangled. Small anisotropies, on the contrary, may decrease the entanglement, which is, in this case, also much affected by the number of excitations. The analysis is made for nearest-neighbor and next-nearest-neighbor defects. The decrease in the entanglement for nearest neighbor defects is not very significant, especially in large chains.
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