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Frustrated quantum spin systems such as the Heisenberg and Kitaev models onvarious lattices, have been known to exhibit various exotic properties not onlyat zero temperature but also for finite temperatures. Inspired by theremarkable development of the quantum frustrated spin systems in recent years,we investigate the finite-temperature properties of the $S=1/2$Kitaev-Heisenberg models on kagome and triangular lattices by means offinite-temperature Lanczos methods with improved accuracy. In both lattices,multiple peaks are confirmed in the specific heat. To find the origin of themultiple peaks, we calculate the static spin structure factor. The origin ofthe high-temperature peak of the specific heat is attributed to a crossoverfrom the paramagnetic state to a short-range ordered state whose static spinstructure factor has zigzag or linear intensity distributions in momentumspace. In the triangular Kitaev model, the "order by disorder" due to quantumfluctuation occurs. On the other hand, in the kagome Kitaev model it does notoccur even with both quantum and thermal fluctuations.

physical review research

Finite-temperature properties of the Kitaev-Heisenberg models on kagome  and triangular lattices studied by improved finite-temperature Lanczos  methods