dorsal/arxiv
View SchemaTwo-spin entanglement distribution near factorized states
| Authors | Fabrizio Baroni, Andrea Fubini, Valerio Tognetti, Paola Verrucchi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702253 |
| URL | https://arxiv.org/abs/quant-ph/0702253 |
| DOI | 10.1088/1751-8113/40/32/010 |
| Journal | J. Phys. A: Math. Theor. 40 9845 (2007) |
Abstract
We study the two-spin entanglement distribution along the infinite $S=1/2$ chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences $C_r$, $r$ being the distance between the two possibly entangled spins, for values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of entanglement, the fraction of such entanglement which is stored in pairwise entanglement, and the way such fraction distributes along the chain is discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length-scale naturally emerges in the system, which is specifically related with entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rule a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of total entanglement, present a smaller fraction of pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on $r$.
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"abstract": "We study the two-spin entanglement distribution along the infinite $S=1/2$\nchain described by the XY model in a transverse field; closed analytical\nexpressions are derived for the one-tangle and the concurrences $C_r$, $r$\nbeing the distance between the two possibly entangled spins, for values of the\nHamiltonian parameters close to those corresponding to factorized ground\nstates. The total amount of entanglement, the fraction of such entanglement\nwhich is stored in pairwise entanglement, and the way such fraction distributes\nalong the chain is discussed, with attention focused on the dependence on the\nanisotropy of the exchange interaction. Near factorization a characteristic\nlength-scale naturally emerges in the system, which is specifically related\nwith entanglement properties and diverges at the critical point of the fully\nisotropic model. In general, we find that anisotropy rule a complex behavior of\nthe entanglement properties, which results in the fact that more isotropic\nmodels, despite being characterized by a larger amount of total entanglement,\npresent a smaller fraction of pairwise entanglement: the latter, in turn, is\nmore evenly distributed along the chain, to the extent that, in the fully\nisotropic model at the critical field, the concurrences do not depend on $r$.",
"arxiv_id": "quant-ph/0702253",
"authors": [
"Fabrizio Baroni",
"Andrea Fubini",
"Valerio Tognetti",
"Paola Verrucchi"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1088/1751-8113/40/32/010",
"journal_ref": "J. Phys. A: Math. Theor. 40 9845 (2007)",
"title": "Two-spin entanglement distribution near factorized states",
"url": "https://arxiv.org/abs/quant-ph/0702253"
},
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