Research On Entanglement Dynamics And Quantum Phase Transition Of One-dimensional Antiferromagnetic Ising System

The solid spin system not only shows rich quantum phase transition,but also has quantum entanglement that is not found in the classical system.The research on equilibrium properties of quantum entanglement and quantum phase transition in the solid spin system has been studied widely.Recently,with the improvement of experimental technology of ultra-cold atomic gas,theorists have begun to explore the non-equilibrium dynamics of quantum entanglement and phase transition in solid spin system.In this paper,by applying quantum renormalization-group method and the concept of negative,the relationship between dynamics of entanglement and quantum phase transition in one-dimensional antiferromagnetic Ising system with Dzyaloshinskii-Moriya(DM)interaction is studied under both types of quantum quench protocols.The stable fixed and quantum phase transition point can be obtained by using the Kadanoff's block renormalization-group method.And we analyze the renormalization flow diagram and the phase transition behavior.It is found that the system exsits a second order phase transition.The analytic expression of the negative can be obtained by using the time evolution operator under both types of quench protocols.The results show that the negative can be obtained by using the time evolution operator.The oscillation behavior of entanglement on both sides of the critical point are the same under the same type of quench protocol when the DM interaction is fixed,but the behavior of the amplitude entanglement on the both sides of the critical point are different with the increase of the system size.And the evolution behavior of entanglement with time and the behavior of entanglement amplitude varying with the scale of the system under both types of quantum quench protocols are different at the left and right side of the critical point when the DM interaction is fixed.When the time is constant,the behavior of entanglement with DM interaction is different under different system scales,but it is found that the entanglement which firstly reaches its maximum under both types of quench protocols is the same.The time which entanglement reaches the maximum firstly and the variation curve of the first derivative of entanglement with DM interaction are given.It is found that the system exsits a second order phase transition.The relationship between the critical exponent of the time and the correlation length is obtained by analyzing the variation behavior of the logarithm of the absolute value of the first derivative of the entanglement with the logarithm of the lattice number of the system.In addition,the analytic expression of the probability of returning to the initial state under both types of quench protocols are analyzed,the behavior of the returning rate near critical point are also different,but the period of the probability of returning to the initial state is the same as theevolution period of entanglement,which can be used as an order parameter to reflect the phase transition behavior of the system.