Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
Oleg Derzhko, Taras Hutak, Taras Krokhmalskii, Jürgen Schnack, Johannes Richter
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 (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 $T\ensuremath{\approx}0.7$. A similar restriction to $T\ensuremath{\gtrsim}0.7$ 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 $T\ensuremath{\approx}0.25$. For the susceptibility $\ensuremath{\chi}(T)$ we find indications of a monotonous increase of $\ensuremath{\chi}$ upon decreasing of $T$ reaching ${\ensuremath{\chi}}_{0}\ensuremath{\approx}0.1$ at $T=0$. Moreover, the EM allows us to estimate the ground-state energy to ${e}_{0}\ensuremath{\approx}\ensuremath{-}0.52$.