  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.
