Low-energy and thermodynamic properties of spin-S Kitaev models

The Kitaev model is an S=1/2 quantum spin model with bond-dependent interactions on a honeycomb lattice and possesses gapless and gapped quantum spin liquids. There are two types of elementary excitations in this model: itinerant Majorana fermions and localized Z₂ fluxes. Moreover, in the case where one of three types of bonds is stronger than the others, the Z₂ fluxes dominate the low-energy physics described by the toric code. While the low-energy properties of the S=1/2 Kitaev model have been studied intensively, features in the extension to higher magnitudes of S remain elusive. In this study, we investigate the finite-temperature properties and anisotropic limit of spin-S Kitaev models. At finite temperatures, the specific heat exhibits the double-peak structure in the S=1/2 Kitaev model due to fractionalization into Majorana and Z₂ quasiparticles. We find that this structure also appears in the higher-S Kiteav models, and the entropy is well scaled by S, which are obtained by calculations using thermal pure quantum states. To clarify the difference by the magnitude of S, we focus on the anisotropic limit of the higher-S Kiteav models. We find that the effective Hamiltonian depends on whether S is integer or half-integer, similar to the Haldane conjecture. The anisotropic Kitaev model is mapped onto the toric code with topological order for the half-integer spin systems but onto a topologically-trivial model for integer spin systems. The result indicates that quantum fluctuations play a crucial role in the ground state, particularly in half-integer systems.