Quantum Entanglement In Spin Systems

Entanglement, first noted by Einstein et. al., is an essential feature of quantum mechanics. It is an exclusive correlation of quantum nature presenting in quantum systems. Besides the conceptual significance in quantum theory, it was rediscovered as a new physical resource to perform numerous tasks in quantum information manipulation in the last decades. Therefore, one of the main tasks of quantum information theory is to quantify the entanglement and the quantum correlations between quantum states. Quantum phase transition (QPT) in an interactive many-body system is the structural change of the ground state. The knowledge about the entanglement and the nonlocal correlation in quantum systems is believed as the key to understand QPTs. In this paper, we investigate the entanglement of a two-spin system with Heisenberg exchange interaction in a quantized field. The pairwise entanglement between bipartite subsystems is obtained. It is shown that the entanglement exhibits a quantum phase transition due to the variation of exchang-couplings. Phase diagrams are obtained explicitly. We also investigate entanglements in spin-1 system with the linear and nonlinear exchange-coupling. The measure of entanglement "Negativity"as a function of the coupling parameterθis calculated explicitly. The entanglement of thermal state as a function of the temperature is discussed. We also have considered the effect of inhomogenous external magnetic field on the entanglement and study the entanglement control.In recent years nanomagnets with higher spin quantum number have attracted more and more attentions due to the potential applications in information storage and quantum computing. The studies of the dimerized SMMs, [Mn4]2, have showed that intermolecular exchange interactions are not always negligible and can instead be used to couple SMMs. These interactions lead to an antiferromagnetic superexchange interaction between the two Mn4 units of the [Mn4]2 dimer. It was pointed out that the supermolecular dimer [Mn4]2 consisting of two molecule magnets Mn4 with antiferromagnetic exchange-coupling exhibits a quite different quantum behavior from two individual Mn4 molecules and may favor the quantum computing [20]. In this paper, we study the entanglement of the supermolecular dimer [Mn4]2 in ground and thermal equilibrium states. Negativity as the measure of entanglement is calculated for various cases.The effect of environment on the quantum system, which may deteriorate the entanglement and even leads to disentanglement, must be taken into account in practical applications. It was shown that entanglement can decay to zero abruptly, in a finite time, know as entanglement sudden death. This surprising phenomenon intrigues great interests. We study the dynamics of two different entanglements, the entanglement of two-qubit system and the entanglement between the system and its environment. A phenomenon of entanglement transfer is also discovered and investigated.