The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.

量子自旋液体在注入空穴时的动力学响应是一个相关的悬而未决的问题。在实验中，在角分辨光电子能谱 (ARPES) 中测量动量分辨或在扫描隧道显微镜 (STM) 中局部测量的空穴光谱函数可用于识别自旋液体材料。在这项研究中，我们采用张量网络方法来模拟掺杂到基塔耶夫自旋液体基态的单空穴的时间演化。着眼于有间隙的自旋液相，我们揭示了两种根本不同的情况。对于铁磁自旋耦合，自旋液体非常容易受到空穴掺杂的影响：即使在弱耦合下，长冈铁磁体也会在掺杂空穴周围动态形成。相比之下，在反铁磁自旋耦合的情况下，空穴谱展示了电荷、自旋和通量自由度之间复杂的相互作用，最好用分段完整子和自旋子的部分子平均场模拟来描述。此外，我们发现我们的数值结果与慢孔的解析可解情况非常吻合。我们的结果表明，动态空穴谱函数提供了有关分级量子自旋液体结构的丰富信息。