Crossover behaviors of entanglement dynamics at the critical point in XXZ spin chain

Abstract

In this paper, we investigate the crossover behaviors of entanglement and return probability at the critical point in one-dimensional XXZ model by quantum renormalization group method. Two types of quench protocols (A) adding the interaction term in z spin direction suddenly and (B) rotating all the even spins by π about the z spin direction suddenly are considered to drive the dynamics of the system, respectively. The dynamical behaviors are closely related to the initial state under two types of quench protocols, especially at N→∞. For the left of critical point, return probabilities eventually approach one under both types of quench protocols. For the right of critical point, return probability oscillates between the maximum value and zero for quench A and tends to one for quench B, respectively. In addition, we discuss the evolution period of entanglement (return probability), find that it is positively and negatively correlated with N in the spin-fluid and Néel phases, respectively. By further analyzing the behaviors of entanglement, return probability and evolution period under both types of quench protocols near the critical point, we observe that they exist the same scaling behaviors, in which the exponents are identical to entanglement exponent of the stationary system, which is related to the results of renormalization group.