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. Pad\'{e} 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 Pad\'{e} approximants, we find ground-state energy $e_{0}=-0.53064\ldots -0.53023$ in good agreement with numerical results. The specific heat $c(T)$ has a typical maximum at rather low temperatures $T\approx0.379$ and the uniform susceptibility $\chi(T)$ at $T\approx0.49$. We also estimate the value of $\chi(T)$ at zero temperature $\chi_{0}\approx0.05\ldots0.06$. The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.