Quantum Entanglement And Magnetic Properties In Low-dimensional Spin Systems

The low-dimensional quantum spin systems, which bridge the quantum information theory and condensed matter physics, have attracted considerable attention for its characteristics of quantum entanglement and magnetic properties.Quantum entanglement, firstly proposed by Einstein et.al., plays an important role in many aspects of applications of quantum computation and quantum information. Furthermore, the quantum entanglement in spin chains have been extensively investigated in condensed matter physics. First, we analyze and discuss the effects of the direction of an external magnetic field and the temperature on entanglement and the dense coding capacity in a two-qubit Ising spin chain. It is found that the entanglement behavior and the maximal dense coding capacity of the system can be varied by controlling the direction of magnetic field. Likewise, it is also different for antiferromagnetic(AF) and ferromagnetic(FM) couplings. Thus, only in a special region for the direction of magnetic field, the optimal dense coding is feasible through the quantum channel.Besides, the effects of direction of magnetic field on. quantum teleportation via a two-qubit Ising spin chain are also discussed. The teleported thermal concurrence and average fidelity can reach a maximum value by controlling the direction of magnetic field. A minimal entanglement of the thermal state is needed to carried out the entanglement teleportation. Nevertheless, the average fidelity is always less than classical limit 2/3, independent of the direction of magnetic field for two-qubit ferromagnetic Ising channel. It is interesting that the entanglement of the channel cannot completely reflect the teleported concurrence and average fidelity. Larger amount of entanglement does not mean better teleportation, for a fixed entanglement corresponding to infinite teleported concurrences or average fidelities.In addition, at a certain temperature, the entanglement in a two-qubit XX chain can reach maximum by adjusting the magnetic field with fixed magnitude to an optimal direction, which can be regarded as magnetic direction induced entanglement.Second, quantum phase transitions (QPTs) which are the evolvements between different ground states of quantum many-body systems, driven solely by quantum fluctuations, play an important role in modern condensed matter physics. Recently, a great deal of effort has been devoted to the understanding of the connection between quantum entanglement and QPTs. For a number of spin systems, it has been shown that QPTs are signaled by a critical behavior of concurrence. However, in general, QPTs can not be detected completely through the analysis of the singularities of concurrence, which are not one-to-one correspondence to the critical points. Herein, the effect of magnetic field on entanglement of a spin-1/2 antiferromagnetic spin ladder with frustration has been investigated. It is found that the concurrence is continuous at the critical point, where the QPT takes place, suggesting no one-to-one correspondence between QPT and the non-analyticity property of the concurrence from another aspect. Moreover, the concurrence shows plateaus in the same region where the magnetization plateaus occur.The third, the multi-spin interactions in low-dimensional quantum spin chains have emerged in the theory study. Such interactions may cause quantum frustration, which eventually leads to the quantum phase transition (QPT) in the system. The spin-1/2 XY chains with three-spin interactions have been studied rigorously. Further considering the influence of four-spin interactions, we show that the two-site entanglement entropy can be exploited as a useful tool to detect the QPTs. In addition to the spin-gapped behavior and incommensurate ferrimagnetic ordering, the "spin waves" modulated by the four-spin interactions is uncovered. The system undergoes the second order QPTs except for the first order QPT occurring at the tricritical point with four-spin couplings.