Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
Abstract
The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys. Ges. 2, 202-204 (1900)] we calculate thermodynamic properties of this model by interpolating between the low- and high-temperature behavior. For that we follow ideas developed in detail by B.~Bernu and G.~Misguich and use for the interpolation the entropy exploiting sum rules [the ``entropy method'' (EM)]. We complement the EM results for the specific heat, the entropy, and the susceptibility by corresponding results obtained by the finite-temperature Lanczos method (FTLM) for a finite lattice of N=32 sites as well as by the high-temperature expansion (HTE) data. We find that due to pronounced finite-size effects the FTLM data for N=32 are not representative for the infinite system below T ≈ 0.7. A similar restriction to T 0.7 holds for the HTE designed for the infinite PHAF. By contrast, the EM provides reliable data for the whole temperature region for the infinite PHAF. We find evidence for a gapless spectrum leading to a power-law behavior of the specific heat at low T and for a single maximum in c(T) at T≈ 0.25. For the susceptibility (T) we find indications of a monotonous increase of upon decreasing of T reaching 0 ≈ 0.1 at T=0. Moreover, the EM allows to estimate the ground-state energy to e0≈ -0.52.