We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor.

中文翻译：

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XXZ链中局部铁电激发后纠缠扩散

我们研究了在XXZ链的基态之上创建的局部铁电激发的时间演化所产生的纠缠的扩展。通过密度矩阵重归一化组计算研究所得的熵分布，并将其与准粒子ansatz进行比较。特别地，我们假设纠缠主要由以不同速度传播的激子激发来进行，并且熵分布通过涉及到达子系统的激子的密度分数的概率表达式来再现。对于适中的XXZ各向异性值，ansatz在无间隙阶段工作良好，最终随着其他类型的准粒子激发获得光谱权重而恶化。此外，如果初始状态被当地的马洛拉那费米子激发，我们观察到熵分布的平凡缩放。在保形场理论框架中进一步研究了这种效应，并为Luttinger液体理论进行了计算。最后，我们还考虑了在链的间隙相中产生反铁磁畴壁的激发，并再次找到具有乘数因子的修饰准拟南芥。