Entanglement in the supermolecular dimer Mn₄₂

This paper investigates the entanglement in the supermolecular dimer Mn₄₂ consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupling J. The conventional von Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M=M₁+M₂=-9 to 0. It is shown that the von Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.