Quantum Entanglement And Quantum Correlation In Heisenberg XY Model On Inhomogeneous Periodic Chain

Quantum information theory has attracted much attention in recent years since it is thecombination of quantum physics and information technologies, its impact is far-reaching,and there will be broad and important application prospects. Quantum entanglement is oneof the important resources in quantum information theory. As a non-localized correlation,there are some fantastic properties that the classical correlation doesn’t have. Based onquantum coherent superposition and quantum entanglement, the proposal of quantumalgorithm has greatly improved the computer efficiency. After the quantum correlation wasstudied in greater depth, a more comprehensive quantum correlation called quantumdiscord has attracted much interest. This article mainly discusses the quantumentanglement and quantum discord of the inhomogeneous periodic Heisenberg XY chain.Firstly, the thermal entanglement and the time-evolution of the entanglement of anisotropic Heisenberg XY chain in an inhomogeneous magnetic field are studied. Theconcurrence is theoretically calculated. The numerical simulation is employed when thenumber of particles in the spin chain is large. If the external magnetic field is small and thenearest neighbor coupling coefficient is large, the concurrence oscillates between0and1.If the external magnetic field is large and the nearest neighbor coupling coefficient is verysmall, the maximum of concurrence decreases and is even disappeared. Meanwhile, as thelength of the Heisenberg spin chain is increased, the entanglement is reduced. When thetemperature is increases, the thermal entanglement will rapidly decrease. As the externalmagnetic field increases, the thermal entanglement also decreases. Only when theinhomogeneity of the system increases, the thermal entanglement can increase.Secondly, the quantum entanglement and quantum discord of an anisotropicHeisenberg XY chain in external inhomogeneous magnetic field is studied. As theparameters are changed, the quantum discord is always greater than the quantumentanglement. The gap between them will decrease with the increasing of the temperature and external magnetic field. The effects of the variation of anisotropic coefficient on bothof them are also evident. The changes of the anisotropic coefficient show that the quantumdiscord may not be zero while the quantum entanglement may be zero. That is, thequantum correlation may exist while the quantum entanglement may disappear.