Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet

Abstract: The $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet allows to study the interplay of geometrical frustration and quantum as well as thermal fluctuations in three dimensions. We use 16 terms of a high-temperature series expansion complemented by the entropy-method interpolation to examine the specific heat and the uniform susceptibility of this model. We obtain thermodynamic quantities for several possible scenarios determined by the behavior of the specific heat as $T\to 0$: A power-law decay with the exponent $\alpha=1,2$ and also $3$ (gapless energy spectrum) or an exponential decay (gapped energy spectrum). All scenarios give rise to a low-temperature peak in $c(T)$ (almost a shoulder for $\alpha=1$) at $T<0.05$, i.e., well below the main high-temperature peak. The functional form of the uniform susceptibility $\chi(T)$ below about $T=0.5$ depends strongly not only on the chosen scenario but also on an input parameter $\chi_0\equiv\chi(T=0)$. An estimate for the ground-state energy $e_0$ depends on the adopted specific scenario but is expected to lie between $-0.441$ and $-0.435$. In addition to the entropy-method interpolation we use the finite-temperature Lanczos method to calculate $c(T)$ and $\chi(T)$ for finite lattices of $N=24$ and $36$ sites. A combined view on both methods leads us to favor the gapless scenario with $\alpha=2$ (but $\alpha=1$ cannot be excluded) and finite $\chi_0$ around $0.1$.