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The pairwise entanglement, measured by concurrence and geometric phase in$d=2,3$-dimensional free-fermion lattice systems have been studied for theground state in this paper. Their derivation with respect to the externalparameter show the singularity closed to the phase transition points, and canbe used to detect the phase transition in this model. Furthermore our studiesshow for the free-fermion model that both concurrence and geometric phase showsthe intimate connection with the correlation functions. The possible relationbetween concurrence and geometric phase has been also discussed.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems