I. INTRODUCTION

Entanglement generation and distribution is one of the important problems in performing quantum-information tasks, such as quantum computation and quantum teleportation. Many results showed that entanglement existed naturally in the spin chain when the temperature is at zero. It is discouraging that the entanglement in many spin systems is typically very short ranged. It exists only in the nearest neighbors and the next nearest neighbors. It is interesting that some schemes for long-range entanglement, such as exploiting weak couplings of two distant spins to a spin chain were proposed. These methods have limited thermal stability or very long time scale of entanglement generation.

In recent years, many researches has shifted the focus of the study in the dynamics of entanglement. The dynamics of long range entanglement are obtained by a time quench of magnetic field. The end-to-end entanglement can be shared across a chain of arbitrary range. It is excited that the most common situations studies so far concerns a sudden quench of some coupling of the model Hamiltonian. In this context, it showed that the long-range entanglement can be engineered by a non-perturbative quenching of a single bond in a Kondo spin chain with impurity. This is the first example that a minimal local action on a spin chain can generate long-range entanglement dynamically. It would be interesting to investigate the possibility of producing long-range entanglement in the XXZ Heisenberg spin chain without impurity.

II. LOCAL QUENCH AND ENTANGLEMENT MEASURE

In this paper, the system is assumed to be in the ground state initially. A local quench change of the coupling between the first qubit and the second qubit with the same anisotropy interaction is performed. The Hamiltonian of the system modifies accordingly. Since the Hamiltonians do not commute, the ground state of the initial Hamiltonian is not one of the eigenstates of the final Hamiltonian. The state of the system will evolve accordingly.

In this paper, the concurrence is chosen as a measurement of the pairwise entanglement. The concurrence is defined as the maximum among the differences calculated from the square roots of the eigenvalues of the related operator. An entirely entangled pair of qubits will have a concurrence of 1, while a pair of non-entangled qubits will have a concurrence of 0.

III. LONG-RANGE ENTANGLEMENT DYNAMICS

The dynamics of entanglement can be difficult to calculate due to the lack of knowledge about the eigenvalues and eigenvectors of the Hamiltonian. For models that are not exactly solvable, most researchers resort to exact diagonalization to obtain the ground state for small system size. However, this method proves difficult when handling larger systems.

A solution to this is applying adaptive time-dependent density-matrix renormalization group (DMRG) on large systems, using a second-order Trotter expansion of the Hamiltonian. Exact diagonalization results can serve as a benchmark to check the accuracy of DMRG for small-sized systems.

The numerical calculations indicate that a sharp drop of long-distance entanglement occurs at certain anisotropic interaction point. Furthermore, the time of the long-range entanglement reaching the maximal value expands drastically. This is similar to the behaviour appeared in referenced works. Moreover, it appears that changing of local interaction from antiferromagnetic to ferromagnetic may enhance the entanglement creation.

The thermalization and relaxation during the period of generating long-distance entanglement are neglected because the dynamical time scale is quite short. When the initial state is taken to be the relevant thermal state, the end-to-end entanglement is plotted as a function of temperature after bond quenching for different system sizes.