Study Of Quantum Correlations In Spin Systems

As a kind of important resources of quantum information and quantum computation, quantum entanglement has inspired research interest in various physical areas of scholars. However, with the development of the study, it was found that quantum correlation can still exist even without entanglement, which also may achieve some accelerated tasks beyond the classical quantum computing. It means that entanglement is not sole quantum correlation that can be used. In order to quantify all of quantum correlations in a state, Ollivier, et al., proposed the concept of quantum discord, which can also characterize the quantum correlation in separated states. Then, the notions of geometric quantum discord, MID and so on have been proposed. It is found that quantum discord and MID are more general quantum resources than entanglement. Because all of these quantum correlations are important resources, it is a very significant thing to analyze them. This paper focus the problem of quantum correlation in spin chain system, the main contents are:1. A two-level qubit coupled with Ising chain independently, in the quantum critical environment, the evolution behavior of quantum discord is more complex than quantum entanglement, there will be periodic steady phenomenon, and the time length of the stability is affected by both the number of particles and the initial spin chain parameters, only selecting the number of particles and the initial parameters appositively can appear the steady phenomenon.2. We analyze the dynamical behaviors of negativity and geometric quantum discord in a qubit and qutrit system. The central qubit (qutrit) is coupled with its own spin-chain environment. The effect of coupled strength g, anisotropy parameter γ, the number of particles N, the initial parameter p and Dzyaloshinsky-Moriya interaction D on evolution of system is investigated and some siganificant results are obtained. In the condition of weak magnetic field, When|-D|≈γ, the effect of delay is most obvious, positive DM strength only plays the role of inhibition. In the case of strong magnetic field, the decay of negativity and geometric quantum discord are characterized by an oscillatory Gaussian envelope, and behave very sensitive with DM effect. What’s more, it is shown that negativity is not always greater that geometric quantum discord, and there is the sudden change point for geometric quantum discord when the proper parameters are chosen. We also find there is no negativity or geometric quantum discord in the separated state, but MID exists with a certain value.3. We study the properties of thermal correlations in qubit-qutrit Heisenberg system. In the weak magnetic field and low temperature, quantum entanglement is larger than geometric quantum discord, the critical temperature of sudden disappearance of quantum entanglement relates to the DM interaction. As the temperature increasing, geometric quantum discord has more chance to survive than entanglement. It is not helpful for quantum correlation in high temperature or strong magnetic or paramagnetic or greater DM interaction. Furthermore, when P=-2D is satisfied with the condition of a small DM interaction, the weak magnetic field and low temperature, the violation of D> N2 is more easily achieved.