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arXiv:1006.1417 · Physical Review A

Quench dynamics of entanglement in an open anisotropic spin- 12 Heisenberg chain

Jie Ren, Shiqun Zhu

Published Jan 21, 2010• 10 citations
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Abstract

The quantum entanglement dynamics of a one-dimensional spin-$1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.

DOI
10.1103/physreva.81.014302

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The quantum entanglement dynamics of a one-dimensional spin-1/21/21/2 anisotropic XXZ\mathit{XXZ}XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.
Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of an one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.
The long-range entanglement dynamics of an one-dimensional spin-1/2 anisotropic XXZ model are studied using the method of the adaptive time-dependent density-matrix renormalization-group. The long-range entanglement can be generated when a local quench on one of boundary bonds is performed in the system. The anisotropic interaction has a strong influence both on the maximal value of long-range entanglement and the time of reaching the maximum long-range entanglement. The local coupling has a notable impact on the long-range entanglement, but it can be neglected in the time of reaching the maximal long-range entanglement.
Abstract. We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and Rényi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction ( ∆ < 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction ( ∆> 0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model. 1.
By using the method of density-matrix renormalization-group theory, the ground-state entanglement in the spin-1/2 isotropic antiferromagnetic Heisenberg chain is studied when there are domain walls generated by a boundary magnetic field. It is found that the pairwise entanglement of odd-bond two qubits decreases and even-bond two qubits increases to stable values alternately when the magnetic field increases. The pairwise entanglement of odd bond can be equal to that of even bond for a suitable value of the magnetic field. When the magnetic field increases further, the entanglement of even bond can be larger than that of odd bond. The entanglement entropy increases and then almost saturates as the number of spin sites increases. Due to the domain walls, the entanglement entropy of even bond decreases to a minimum value and then increases as the magnetic field increases.
We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and Rényi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction (Δ< 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction (Δ>0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model.
We investigate the dynamics of the XXZ spin chain after a geometric quench, which is realized by connecting two half chains prepared in their ground states with zero and maximum magnetizations, respectively. The profiles of magnetization after the subsequent time evolution are studied numerically by density-matrix renormalization group methods, and a comparison to the predictions of generalized hydrodynamics yields a very good agreement. We also calculate the profiles of entanglement entropy and propose an ansatz for the noninteracting XX case, based on arguments from conformal field theory. In the general interacting case, the propagation of the entropy front is studied numerically both before and after the reflection from the chain boundaries. Finally, our results for the magnetization fluctuations indicate a leading order proportionality relation to the entanglement entropy.