Vison-Majorana complex zero-energy resonance in Kitaev's spin liquid

We study the effect of site dilution in Kitaev's model. We derive an analytical solution of the dynamical spin correlation functions for arbitrary configurations of $Z_2$ fluxes. By incorporating this solution into classical Monte Carlo scheme, we address how a site vacancy affects the experimental observables, such as the static spin susceptibility and the spin lattice relaxation rate, $1/T_1$. As a result, we found an enhancement of dynamical magnetic response in the vicinity of vacancy, which leads to Friedel-like oscillation in local $1/T_1$, in contrast to limited influences on the static susceptibility. Furthermore, we found a sharp zero-energy peak in the magnetic excitation spectrum, which is attributed to the Vison & Majorana zero mode trapped near the site vacancy. This zero mode can be interpreted as fractionalized spin hole into an Ising triplet with differentiated magnetic axes, which leads to the characteristic temperature and field-orientational dependence of $1/T_1$.