  We investigate the impact of two types of disorder, bond randomness and site
dilution, on the spin dynamics in the Kitaev model on a honeycomb lattice. The
ground state of this model is a canonical quantum spin liquid with spin
fractionalization into two types of quasiparticles, itinerant Majorana fermions
and localized fluxes. Using unbiased quantum Monte Carlo simulations, we
calculate the temperature evolution of the dynamical spin structure factor, the
magnetic susceptibility, and the NMR relaxation rate. In the dynamical spin
structure factor, we find that the two types of disorder affect seriously the
low-energy peak dominantly originating from the flux excitations, rather than
the high-energy continuum from the Majorana excitations, in a different way:
The bond randomness softens the peak to the lower energy with broadening,
whereas the site dilution smears the peak and in addition develops the other
sharp peaks inside the spin gap including the zero energy. We show that the
zero-energy spin excitations, which originate from the Majorana zero modes
induced around the site vacancies, survive up to the temperature comparable to
the energy scale of the Kitaev interaction. For the bond randomness, the
low-temperature susceptibility does not show any qualitative change against the
weak disorder, but it changes to divergent behavior while increasing the
strength of disorder. Similar distinct behaviors for the weak and strong
disorder are observed also in the NMR relaxation rate; an exponential decay
changes into a power-law decay. In contrast, for the site dilution, we find no
such crossover; divergent behavior in the susceptibility and a power-law decay
in the NMR relaxation rate appear immediately with the introduction of the site
dilution. We discuss the relevance of our results to experiments for the Kitaev
candidate materials with disorders.
