Entanglement, quantum phase transition, and scaling in the XXZ chain -: art. no. 042330

Motivated by recent development in quantum entanglement, we study relations among concurrence C, SUq(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possesses the maximum concurrence. When the anisotropic parameter Delta is deformed, however, its value decreases. Its dependence on Delta scales as C = C-0 - C-1 (Delta - 1)(2) in the XY metallic phase and near the critical point (i.e., 1 <Delta < 1.3) of the Ising-like insulating phase. We also study the dependence of C on the correlation length xi, and show that it satisfies C = C-0 - 1/2xi near the critical point. For different sizes of the system, we show that there exists a universal scaling function of C with respect to the correlation length xi.