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 of 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,
|Ψ⟩ = (((2)1/2)/2)(|01⟩-|10⟩), is
maximum entanglement. For the XXZ chain, when Γ→∞, the concurrence will meet its maximum value
max = (sinh (1/T))/(cosh (1/T)).