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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., Comment: 14 pages, 32 figures, revtex4

In this paper we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimenion. Entanglement can be classified in the framework of the scaling theory of phase transition. There is a profound difference between the classical correlations, whose correlation length diverges at the phase transiton, and non-local quantum correlations that remain, in general, short ranged.