Vanishing Wilson ratio as the hallmark of quantum spin-liquid models

We present numerical results for finite-temperature $T>0$ thermodynamic quantities, entropy $s(T)$, uniform susceptibility $\chi_0(T)$ and the Wilson ratio $R(T)$, for several isotropic $S=1/2$ extended Heisenberg models which are prototype models for planar quantum spin liquids. We consider in this context the frustrated $J_1$-$J_2$ model on kagome, triangular, and square lattice, as well as the Heisenberg model on triangular lattice with the ring exchange. Our analysis reveals that typically in the spin-liquid parameter regimes the low-temperature $s(T)$ remains considerable, while $\chi_0(T)$ is reduced consistent mostly with a triplet gap. This leads to vanishing $R(T \to 0)$, being the indication of macroscopic number of singlets lying below triplet excitations. This is in contrast to $J_1$-$J_2$ Heisenberg chain, where $R(T \to 0)$ either remains finite in the gapless regime, or the singlet and triplet gap are equal in the dimerized regime.