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Entanglement in One-Dimensional Spin Systems

A. Osterloh·L. Amico·F. Plastina·R. Fazio
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Abstract

For the anisotropic XY model in transverse magnetic field, we analyze the ground state and its concurrence-free point for generic anisotropy, and the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. A transmutation from singlet-like to triplet-like states is observed during the propagation. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The ``entanglement wave'' evolving from a Bell state on the ground state turns out to be very localized in space-time. Our findings agree with a recently formulated conjecture on entanglement sharing; some results are interpreted in terms of this conjecture.

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A. Osterloh, L. Amico, F. Plastina, R. Fazio. 2006-04-24. Entanglement in One-Dimensional Spin Systems. https://doi.org/10.1117/12.542337

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