Approach to the quantum phase transition of spin chains in terms of pair-wise entanglement

The Lewenstein-Sanpera decomposition of a two-qubit density matrix ρ provides us with a clear understanding of the entanglement properties in S=1/2 quantum Ising spin chains undergoing quantum phase transition (QPT). By decomposing ρ into a separable part Λρs and an inseparable part (1−Λ)ρe, we can evaluate the concurrence C(ρ), a measure of pair-wise entanglement, as a product of 1−Λ and the concurrence C(ρe). By analyzing 1−Λ and C(ρe), we can interpret the reported singular behavior of C(ρ) in the conventional QPT framework. The behavior of C(ρe) and 1−Λ at the critical point indicates the singular maximization of quantum spin fluctuation and the divergence in the spin correlation length, respectively.