Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
We study the spin-
S Kitaev model in the classical ($S\ensuremath{\rightarrow}\ensuremath{\infty}$) limit using Monte Carlo simulations combined with semiclassical spin dynamics. We discuss differences and similarities in the dynamical structure factors of the spin-
1/2 and the classical Kitaev liquids. The quantum behavior is restricted to low temperatures where a gap protects visons from decohering the system. Once this quantum gap is breached, at low temperatures compared to the coupling constant, significant entropic disorder decoheres the Majorana fermions and the system is described quantitatively by classical dynamics. The low-temperature and low-energy spectrum of the classical model exhibits a finite-energy peak, which is the precursor of the one produced by the Majorana modes of the
S=1/2 model. The classical peak is spectrally narrowed compared to the quantum result and can be explained by magnon excitations within fluctuating one-dimensional manifolds (loops). Hence the difference from the classical limit to the quantum limit can be understood by the fractionalization of magnons propagating in one-dimensional manifolds. Moreover, we show that the momentum-space distribution of the low-energy spectral weight of the
S=1/2 model follows the momentum-space distribution of zero modes of the classical model.
The Kitaev model is a unique exactly solvable two-dimensional quantum spin system that exhibits a spin-liquid ground state. Here, the authors rigorously rederive and extend a Majorana mean-field theory approach that reproduces, but applies beyond, the exact results. The authors use this approach to predict inelastic neutron scattering (INS) results on realistic Hamiltonians of hypothetical Kitaev spin-liquid materials. Not limited to just the Kitaev model, this approach can extend the applicability of mean-field theory in analyzing dynamics for any system without a large coordination number.