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International Journal of Modern Physics B

CREATION OF QUANTUM ENTANGLEMENT IN SPIN-ONE ISING MODEL WITH LONGITUDINAL AND TRANSVERSE CRYSTAL FIELDS

Ming‐Liang Hu

Published Nov 10, 2010• 2 citations
Publisher

Abstract

We study ground-state pairwise entanglement of spins in mean field clusters of spin-one particles interacting via the Ising interaction in the presence of longitudinal and transverse crystal fields. A general result is found that for all kinds of the spin-one Ising models, the pairwise negativities are symmetric with respect to the zero values of the applied transverse or longitudinal magnetic fields. For models considered in this paper, we show numerically that the crystal fields can serve as an alternative tool to create "on-demand" ground-state entanglement for small clusters of spins.

DOI
10.1142/s021797921005692x

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We study ground-state pairwise entanglement of spins in mean field clusters of spin-one particles interacting via the Ising interaction in the presence of longitudinal and transverse crystal fields. A general result is found that for all kinds of the spin-one Ising models, the pairwise negativities are symmetric with respect to the zero values of the applied transverse or longitudinal magnetic fields. For models considered in this paper, we show numerically that the crystal fields can serve as an alternative tool to create "on-demand" ground-state entanglement for small clusters of spins.
We study the phase diagram and magnetic properties of a transverse spin-1 Ising model with random longitudinal crystal-field interactions using an expansion technique for cluster identities of spin-1 localized spin systems. Partially ordered phases appear for a particular two valued distribution P(D i )=1/2( delta (D i -(1+ alpha )D)+ delta (D i -(1- alpha )D)), and sufficiently small transverse field Omega . The longitudinal and transverse magnetizations and the quadrupolar moments are calculated. General formulae, applicable to structures with arbitrary coordination number N, are given.
We consider the ground state of the one-dimensional quantum Ising model with transverse field hx in one dimension depending on the site x∈Z in a finite volume Λm ≔ {−m, −m + 1, …, m + L}. We make suitable assumptions on the regions where the field is small and prove that if the field is sufficiently large on the complementary set, then the entanglement of the interval Λ0≔0,..,L relative to its complement Λm\Λ0 is bounded uniformly in m and L. The result applies in particular to periodic transverse fields. The bound is established by means of a suitable cluster expansion.