Entanglement, Decoherence And Quantum Phase Transition In Low-Dimensional Spin Chain

Recently, as one of the most activity topics, quantum information physics attracts much attention in many branches of physics both in theoretical aspects and experimental ones. In this thesis, we focus the topic on the quantum entanglement, decoherence and quantum phase transitions in the low-dimensional spin systems.It is interesting and valuable to investigate and manipulate the entanglement characters in the spin cluster model. First, we have investigated the entanglement behavior in the Heisen-bergⅩⅩⅩspin chain with impurity. The results reveal that we can induce entanglement in this system by controlling a properly impurity parameter both in the ferromagnetic case and anti-ferromagnetic ones no matter whether there is external magnetic field or not. Moreover, we find that it is possible to enhance the temperature Tc where the entanglement vanishes. Second, we study the role of two kinds of multi-site interactions (XZY—YZX type and XZX+YZY type) to the entanglement in the Heisenberg XXZ spin chain. The results have demonstrated that the roles of XZY-YZX type interaction to the entanglement are identical to the role of Dzyaloshinsky-Moriya(DM) interaction. Furthermore, we find that the direction of the external magnetic field can play a different role in the entanglement when the multi-site XZX+YZY type interaction emerges. We also study the entanglement property against various parameters (temperature T, external magnetic field B, and anisotropy Jz).The interaction between the quantum system and its environment leads to decoherence of the entanglement, which is a major obstacle for building a practical quantum processor. This complex quantum many-body phenomenon is challenging and many models both for correlated and uncorrelated environments have been dealt with. In the second part, we study the dynamical entanglement from spin environment. For the case of two qubits coupled to an environment described by a XY spin chain with DM interaction, the results showed that the DM interaction can enhance slightly the decay of the decoherence factor in the weak coupling region. However, in the strong coupling region, the decoherence factor is super-sensitive to the DM interaction. For the three qubits ones, if the initial state is with W, we find that the DM interaction can enhance slightly the decay of entanglement both in the weak coupling region and strong coupling one. If the initial state is with GHZ, the decay of entanglement is very sensitive to the DM interaction in the strong coupling region.We also study the dynamical entanglement of two spin qubits coupled to an XY spin-chain with the three-site interaction environment. The dynamical process of disentanglement is numerically and analytically investigated. In the strong coupling region, we find that the three-site interaction can dramatically accelerate the decay of the entanglement between the two spin qubits. However, in the weak coupling region, the role of this interaction in the process of disentanglement depends on the strength of the three-site interaction, e.g., in some specific intervals, this interaction can delay remarkably the process of disentanglement.Quantum phase transition (QPT) is a well addressed topic in the condensed physics. Tra-ditionally, QPT is described in the framework of order parameter and symmetry breaking within the Landau-Ginzburg paradigm. In the third part, we pay attention to this problem from the quantum-information perspective and study the quantum phase transition in a XY spin chain with multi-site interaction in the framework of quantum information theory (fidelity susceptibility and geometrical phase). The key ingredients (e.g, finite-size scaling behavior, universality principle) of the quantum criticality near the critical point are investigated care-fully. The results show that both the fidelity susceptibility and geometrical phase are reliable to characterize the quantum critical behaviors and the multi-site interaction can induce the redistribution of the criticality region. Moreover, both of them give rise to the same phase diagram.