Thermodynamics of the $S=1/2$ maple-leaf Heisenberg antiferromagnet

Abstract

The Heisenberg antiferromagnet on the maple-leaf lattice has recently gathered a great deal of attention. Competition between three nonequivalent bond interactions results in various ground-state quantum phases, the exact dimer-product singlet ground state being among them. The thermodynamic properties of this model are much less understood. We used high-temperature expansion up to the $18$th order to study the thermodynamics of the $S=1/2$ Heisenberg model on the uniform maple-leaf lattice with the ground state exhibiting a six-sublattice $120^{\circ }$ long-range magnetic order. Padé approximants allow us to get reliable results up to the temperatures of about $T\approx 0.4$. To study thermodynamics for arbitrary temperatures, we made the interpolation using the entropy method. Based on the analysis of close Padé approximants, we find ground-state energy $e_0=-0.53064\dots -0.53023$ in good agreement with numerical results. The specific heat $c(T)$ has a typical maximum at rather low temperatures $T\approx 0.379$ and the uniform susceptibility $\chi (T)$ at $T\approx 0.49$. We also estimate the value of $\chi (T)$ at zero temperature ${\chi }_0\approx 0.05\dots 0.06$. The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.

9 pages, 5 figures