Entanglement of Two-Qubit Quantum Heisenberg XYZ Chain

We derive the analytic expression of the concurrence in the quantum Heisenberg XYZ model and discuss the influence of parameters J, Δ, and Γ on the concurrence. By choosing different values Γ and Δ, we obtain the XX, XY, XXX and XXZ chains. The concurrence decreases with increasing temperature. When T → 0, the concurrence reaches its maximum value 1, i.e., the entangled state, | > = √2/2 (|01> - |10>), is maximum entanglement. For the XXZ chain, when Γ → ∞, the concurrence will meet its maximum value C_max = sinh(1/T)/cosh(1/T).