24-02E

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 the S = 1/2 hyperkagome-lattice Heisenberg antiferromagnet. We obtain thermodynamic quantities for the two possible scenarios of either a gapless or a gapped energy spectrum. We have found that the specific heat c exhibits, besides the high-temperature peak around T ≈ 0.669, a low-temperature one at T ≈ 0.021–0.033. The functional form of the uniform susceptibility χ below about T = 0.5 depends strongly on whether the energy spectrum is gapless or gapped. The value of the ground-state energy can be estimated to e₀ ∈ [–0.440,–0.435]. In addition to the entropy-method interpolation we use the finite-temperature Lanczos method to calculate c and χ for finite lattices of N = 24 and 36 sites. A combined view on both methods leads us to favour a gapless scenario since then the maximum of the susceptibility at T ≈ 0.118–0.194 agrees better between both methods.