Quenching Dynamics Of Quantum Entanglement On XXZ Spin Chains

Solid-state quantum spin systems exhibit peculiar and rich phase transition behaviors,which can be used to research quantum entanglement,quantum correlation and quantum phase transitions in quantum spin systems at equilibrium state.Recently,the non-equilibrium evolution of solid-state quantum spin systems become a common focus in the field of statistical physics and quantum information with the advancement of experimental techniques such as super-cooled quantum gas and ultra-fast pulsed laser.In this paper,the quench dynamics of quantum entanglement in the XXZ spin chain is studied using the method of quantum renormalization group,and we devote to exploring the effects of different quantum quenching protocols on the evolution of the system entanglement.The transformation equation of XXZ spin chain is obtained using the Kadanoff's block method and then the critical point of the system is obtained.The time evolution operator is used to obtain the analytic expression of the concurrence of the system for different types of quench,they are recorded asC₁?t?andC₂?t?,respectively,and they are found to be the function of anisotropy parameters and time.The relationship between concurrence and anisotropy parameters and time is analyzed under two different quenching protocols?initial conditions?.It is found that both ofC₁?t?andC₂?t?are periodic functions with respect to time for a given value of anisotropic parameter and they have the same period,but their evolution behavior is very different.When the time is a certain value,we find that the changes ofC₁?t?andC₂?t?with respect to anisotropic parameters are quite different.Moreover,the short-time and long-time behavior of concurrence is somewhat different.It is shown that the initial conditions have an important influence on the evolution of the system entanglement.However,Increasing the chain length enhances the oscillation theC₁?t?andC₂?t?,and they all occur drastic change when they cross the quantum critical point.For any anisotropic parameter value,there are two characteristic time(T_minandT_max)at which theC₁?t?reaches its the first minimum and the C₂?t?reaches its the first maximum,respectively,it is found thatT_minandT_maxare the analytic functions with respect to the coupling?.We find that the change of the characteristic time versus?for different QRG steps cross each other at the critical point,and both of theT_minin andT_maxdevelop two saturated values when the number of particles tends to infinity.The minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior with exponent which corresponds to the entanglement exponent for the one-dimensional XXZ model in equilibrium,in particular,the scaling behavior near the critical point is independent of the quench type or initial state.It is shown that the characteristic time can be used to describe the quantum critical properties of the one-dimensional XXZ model,and this description is universal.