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Chinese Physics B

Effects of quantum quench on entanglement dynamics in antiferromagnetic Ising model

Yue 玥 Li 李, Panpan 盼盼 Fang 房, Zhe 哲 Wang 王, Panpan 盼盼 Zhang 张, Yuliang 玉良 Xu 徐, Xiangmu 祥木 Kong 孔

Published Jun 25, 2023• 1 citation
Publisher

Abstract

We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya (DM) interaction by using the quantum renormalization-group method and the definition of negativity. Two types of quench protocols (i) adding the DM interaction suddenly and (ii) rotating the spins around x axis are considered to drive the dynamics of the system, respectively. By comparing the behaviors of entanglement in both types of quench protocols, the effects of quench on dynamics of entanglement are studied. It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors. Especially, the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system. In addition, the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.

DOI
10.1088/1674-1056/ace15c

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We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya (DM) interaction by using the quantum renormalization-group method and the definition of negativity. Two types of quench protocols (i) adding the DM interaction suddenly and (ii) rotating the spins around x axis are considered to drive the dynamics of the system, respectively. By comparing the behaviors of entanglement in both types of quench protocols, the effects of quench on dynamics of entanglement are studied. It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors. Especially, the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system. In addition, the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.
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.
"We have studied the quantum phase transition of the Ising model with Dzyaloshinsky-Moriya (DM) interaction, by means of measures of entanglement as concurrence and von Neumann entropy. The study was performed using the Density Matrix Renormalization Group (DMRG). The parameter which drives the phase transition in this model is the D, which accounts for the strength of the DM interaction. The model has two phases, an antiferromagnetic phase and a chiral saturated phase, with critical point D = 1. By calculating the entanglement measures for both, open and periodic boundary conditions it was found that the critical point is signaled by an extreme behavior of the entanglement measure, maximum or minimum, it was also found these measures seem to tend to an asymptotic value when D → ∞ representing the chiral saturated phase."
We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.
By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.