Similarity of thermodynamic properties of the Heisenberg model on triangular and kagome lattices

Derivation of a reduced effective model allows for a unified treatment and discussion of the ${J}₁\text{\ensuremath{-}}{J}₂\phantom{\rule{4pt}{0ex}}S=1/2$ Heisenberg model on triangular and kagome lattices. Calculating thermodynamic quantities, i.e., the entropy $s(T)$ and uniform susceptibility ${\ensuremath{\chi}}₀(T)$, numerically on systems up to effectively $N=42$ sites, we show by comparing to full-model results that low-$T$ properties are qualitatively well represented within the effective model. Moreover, we find in the spin-liquid regime similar variation of $s(T)$ and ${\ensuremath{\chi}}₀(T)$ in both models down to $T\ensuremath{\ll}{J}₁$. In particular, studied spin liquids appear to be characterized by the Wilson ratio vanishing at low $T$, indicating that the low-lying singlets are dominating over the triplet excitations.