Quantum Correlation And Entanglement Dynamics In XXZ Spin Systems

As important concepts in quantum mechanics,Quantum correlation and quantum entanglement have important application values in quantum information and quantum computation.They can also be used to characterize the quantum phase transitions of the quantum multibody spin systems,which is essentially related to the quantum phase transition of the systems.At present,most of the researches focus on the equilibrium systems,and there are relatively few researches on the nonequilibrium dynamic systems.In this thesis,based on the study of thermal entanglement in the mixed-spin system,the quantum correlation of the antiferromagnetic XXZ model on the fractal lattices and the entanglement dynamics of the one-dimensional XXZ model are studied.The main contents of this dissertation are as follow:1.The thermal entanglement of the mixed-spin XY system with two and three sites are investigated.It is found that both ferromagnetic or antiferromagnetic cases,the negativity of systems decreases with increasing temperature and finally changes to zero smoothly.And the temperature T0(defined as the characteristic temperature)at which the negativity becomes zero is low when the value of the crystal field parameter D is large.In addition,the ground-state entanglement of the system is studied and compared with thermal entanglement(T?0).It is found that when T?0 the mixed-state entanglement and the thermal entanglement can be well corresponding in both systems studied.But in the two-sites system,the entanglement of pure state and mixed state is quite different;in a three-sites system,the pure state entanglement is the same as the mixed state entanglement.2.The quantum correlations between two non-nearest-neighbor end spins in the antiferromagnetic XXZ model on diamond-type hierarchical lattices with fractal dimensions of 1.63,2 and 2.58 are studied.For the system with fractal dimension of 1.63,we directly apply the decimation renormalization group(RG)method to deal with it.But for the systems with dimensions of 2 and 2.58,we first use the equivalent transformation to equivalent the antiferromagnetic systems to the ferromagnetic systems,and then use the RG method to deal with them.We use quantum discord(QD)to measure the quantum correlation and discuss the relations of QD with temperature T,anisotropic parameter? and lattice number L.By analyzing the contour plots of QD,the continuous relations of it with T and ? are obtained.It is found that QDs in the three lattices have maximum values at T=0,and decrease gradually with increasing T.They decrease with the increase of ? and there is a turning point at the critical point ?=0,where there is a "peak" of the contour line.No matter how large the size of system is,QDs will change to 0 when ?= 1.In addition,they decrease with the increase of lattice number L in general.For the system with fractal dimension of 1.63,QD is almost zero when L?30;For the systems with fractal dimensions of 2 and 2.58,they still exist when L is large.3.Using the Kadanoff block RG method,it is studied that the relationship of quantum entanglement with time and anisotropy parameter ? of the XXZ model on a one-dimensional spin chain for two quenching protocols.The difference between two entanglements(entanglement of site 1 and site 2,respectively)is discussed by using partial entropy entanglement to measure the entanglement.It is found that the two entanglements vary periodically with time for the two quenching protocols.And with the increase of N sites,the anisotropic parameter ? gradually approach the stable fixed point ?=0 and the period of system increased at the left of the critical point(?=0.9);At the critical point(?=1),the period of entanglement over time is independent of N;At the right of the critical point(?=1.1),? gradually approach the stable fixed point?=? and the period decreased.When the time is constant,quantum entanglement shows different oscillation forms with the change of anisotropic parameters ?,which is related to the different initial states caused by the two quenching protocols.However,as the anisotropy parameter increases,the amplitudes of entanglement are decrescent.As N increases,the position where entanglement reaches the maximum or mininum values for the first time gradually approach the critical point.