Entanglement in a second order quantum phase transition

Abstract

We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point ${\lambda }_c$, in the thermodynamic limit. We also show that there exists a value ${\lambda }_0\ge {\lambda }_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.

4 pages, 4 EPS figures, minor corrections added and title changed

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• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
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