Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate

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, for which the spin dynamics provides a good probe of the fractionalization. Using unbiased quantum Monte Carlo simulations, we calculate the temperature evolution of the dynamical spin structure factor, the magnetic susceptibility, and the nuclear magnetic resonance (NMR) relaxation rate while changing the strength of disorder systematically. In the dynamical spin structure factor, we find that the two types of disorder seriously affect the low-energy peak originating dominantly 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, which suggests the closing of the spin gap, 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. We also find that the two types of disorder affect the low-temperature behavior of the magnetic susceptibility and the NMR relaxation rate in a different way. 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. We find that this crossover corresponds to the softening of the low-energy peak in the dynamical structure factor. Similar distinct behaviors for the weak and strong disorders are also observed 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 immediately appear with the introduction of the site dilution, which is also attributed to the emergence of the Majorana zero modes. We discuss the relevance of our results to experiments for the Kitaev candidate materials with disorders. The peculiar magnetic responses found by the present systematic analysis would be helpful to not only identify the dominant type of disorder in real materials but also examine the experimental realization of the Kitaev spin liquid by introducing disorder.

Automated summary

The study investigates the impact of two types of disorder on spin dynamics in the Kitaev model on a honeycomb lattice, revealing that disorder affects the energy spectrum of spin excitations, including peaks from flux and Majorana excitations. Different types of disorder have distinct effects on the low-temperature behavior of the magnetic susceptibility and NMR relaxation rate.