Thermal Fractionalization in Kitaev Quantum Spin Liquids*

The quantum spin liquid is an exotic state in insulating magnets, where conventional magnetic ordering is suppressed down to the lowest temperature by quantum fluctuations. Among the salient features is the fractionalization of quantum spins into emergent quasi-particles, such as spinons. Despite tremendous efforts for several decades, it is hard to identify the clear evidence of spin fractionalization in real materials. Most of such efforts have been done for asymptotic behaviors toward zero temperature, but they remain elusive due to extrinsic contributions inevitable at low temperatures. We here discuss more versatile signatures of the spin fractionalization in a wider temperature range, by taking the honeycomb Kitaev model. The Kitaev model provides an exact ground state being a quantum spin liquid, in which spins are fractionalized into itinerant Majorana fermions and localized Z₂ fluxes. The model has attracted much attention since it is experimentally relevant to magnetic insulators with strong spin-orbit coupling, such as A₂IrO₃ and α-RuCl₃. Beyond the exact ground state, we have investigated the static and dynamical properties of the Kitaev model at finite temperature, by developing new numerical techniques based on a Majorana fermion representation. We have unveiled the fingerprints of spin fractionalization in the temperature and energy dependences of various physical observables, such as the specific heat, magnetic susceptibility, NMR relaxation rate, dynamical spin structure factor, Raman scattering, and thermal transport. We will discuss the results in comparison with recent experimental data for the candidate materials. For references, visit http://www.motome-lab.t.u-tokyo.ac.jp/publication-e.html.