Entanglement in a second-order quantum phase transition

Abstract

We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes 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 cusplike singularity appears at the critical point ${\ensuremath{\lambda}}_{c}$ in the thermodynamical limit. We also show that there exists a value ${\ensuremath{\lambda}}_{0}>~{\ensuremath{\lambda}}_{c}$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.