Quantum Correlations In The Heisenberg Spin Chain

Recently, quantum correlation was analyzed in a great number of research paper, for example, spin-chain model, open quantum system, quantum dots, and biological system. Specially the quantum discord presented in Heisenberg spin chain models with various factors such as temperature, anisotropies, magnetic field and so on, has been studied qualitatively and quantitatively. It has been shown that Dzyaloshinski-Moriya (DM) interaction which arises from spin-orbit interaction in spin-chain system can enhance the critical temperature and fidelity for entanglement. Naturally we will query the effect of DM interaction on quantum correlation. Moreover, due to the inevitable interaction with the environment, it is necessary to take decoherence into account for quantum state in quantum information processing. Here we consider the dissipative dynamics of QD in the environment with Ornstein-Uhlenbeck noise.First, we investigate quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing Dz increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decrease QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.Second, We investigate quantum discord of a three-qubit Heisenberg XXZ system with DM interaction parameter. We find that both DM interaction parameter Dz and anisotropic parameter Jz can increase QD and entanglement but D2is a more efficient parameter in antiferromagnetic case. We observe a complex range of QD with the change of Dz and a sudden change of QD with the variation of Jz in ferromagnetic case. By controlling Dz and Jz synchronously, we can get the maximum of QD.Third, Then we calculate the three-qubit quantum discord and quantum entanglement under Ornstein-Uhlenbeck noise. In evolutionary process, entanglement decreases faster than QD and occurs sudden death while QD only vanishes in asymptotic limit. The decrease of both QD and entanglement can be prolonged by the increase of DM interaction and the decrease of the noise bandwidthγ. In addition, we find that QD may be more practical and robust than entanglement as a resource of information.