We numerically study the real-time dynamics of a single hole created in the $t-J$ model on a square lattice. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on the Bethe lattice. Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics.

中文翻译：

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二维量子反铁磁体中磁极化子的动力学形成

我们数值研究了在方格上的 $tJ$ 模型中创建的单个孔的实时动力学。最初，孔以与跳跃矩阵元素成正比的速度弹道传播。在中长时间内，维度以及自旋背景决定了孔动力学。在二维量子反铁磁体的基态中产生的空穴在很长一段时间内再次弹道传播，但速度与自旋交换耦合成正比，这表明磁极化子的形成。我们根据部分构造提供了对这种动力学的直观解释，这与数值模拟具有良好的定量一致性。在无限温度和无自旋交换耦合的限制下，动力学可以通过 Bethe 晶格上的量子随机游走来近似。添加 Ising 相互作用对应于有效的无序势，这可以显着减慢空穴传播，与亚扩散动力学一致。