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

Abstract

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 Λ ρ s and an inseparable part ( 1 − Λ ) ρ e , we can evaluate the concurrence C ( ρ ) , a measure of pair-wise entanglement, as a product of 1 − Λ and the concurrence C ( ρ e ) . By analyzing 1 − Λ and C ( ρ e ) , we can interpret the reported singular behavior of C ( ρ ) in the conventional QPT framework. The behavior of C ( ρ e ) and 1 − Λ at the critical point indicates the singular maximization of quantum spin fluctuation and the divergence in the spin correlation length, respectively.