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 $J_1\text{−}{J}_{2}S=1/2$ Heisenberg model on triangular and kagome lattices. Calculating thermodynamic quantities, i.e., the entropy $s\left(T\right)$ and uniform susceptibility ${\chi }_0\left(T\right)$, 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 $s\left(T\right)$ and ${\chi }_0\left(T\right)$ in both models down to $T\ll J_1$. 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.

Figure 1

(a) Triangular and (b) kagome lattice represented as the (triangular) lattices of coupled basic triangles. Shown also are model exchange couplings on both lattices.

Figure 2

Results for the effective model (EM) for the triangular lattice, compared with the full HM. All results are for $N=30$ sites [60]: (a) for entropy density $s\left(T\right)$ and (b) uniform susceptibility ${\chi }_0\left(T\right)$. (c) and (d) The same quantities for the kagome lattice, compared to the full HM, all on $N=42$ sites [50].

Figure 3

Results within the EM on a triangular lattice for different $J_2=0,0.1,0.15$; (a) for $s\left(T\right)$ and (b) for ${\chi }_0\left(T\right)$.

Figure 4

Results within the EM on a kagome lattice for different $J_2=0,0.2,0.4$; (a) for $s\left(T\right)$ and (b) for ${\chi }_0\left(T\right)$.

Figure 5

Wilson ratio $R\left(T\right)$, evaluated from $s\left(T\right)$ and ${\chi }_0\left(T\right)$ for the full HM on a square lattice, a triangular lattice with $J_2=0,0.1$ [60], and a kagome lattice [50]. Results are presented for $T>T_{\text{fs}}$.

Figure 6

$R\left(T\right)$, evaluated within the EM for (a) TL with $J_2=0,0.1,0.15$, and (b) KL for $J_2=0,0.2,0.4$.