Critical entropy of quantum Heisenberg magnets on simple-cubic lattices

Abstract

We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)kB , whereas for the ferromagnet, a larger value of 0.401(5)kB is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic Néel state in ultra-cold fermion gases in optical lattices.

Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices

“…We thank S. Wessel for providing us with the entropy data of the Heisenberg model from Ref. [26]. We acknowledge discussions and previous collaborations on related subjects with I. Bloch, the group of T. Esslinger, F. Gerbier, E. Gull, M. Köhl, J. Oitmaa, L. Pollet, A. Rosch, C. Salomon, and M. Troyer.…”

“…This value also corresponds to the mean-field value for the entropy of the Heisenberg model in its paramagnetic phase. In reality, the value of the entropy is reduced by short-range antiferromagnetic correlations [26]. In Fig. 14, this limitation of single-site DMFT is exposed as we compare entropy obtained with DMFT to the ones given by the series expansion and the Heisenberg model.…”

“…The Pade expansion of the high-temperature series expansion lies slightly above the entropy of the Heisenberg model calculated in Ref. [26] by QMC simulations. This situation represents a case in which the high-temperature expansion can be used down to a lower temperature than single-site DMFT.…”

“…As DMFT neglects spatial correlations in the paramagnetic phase, within this theory, the decrease in entropy only happens right at the Néel transition where long-range antiferromagnetic order sets in (this Néel transition occurs at a lower temperature than the ones studied in the present paper). However, in reality, the entropy will start deviating significantly from ln 2 above the Néel transition, as short-range correlations develop [16,[24][25][26]. Nevertheless, the single-site DMFT description can be regarded as a good description of the paramagnetic Mott insulator down to a characteristic temperature.…”

Thinking locally: Reflections on Dynamical Mean‐Field Theory from a high‐temperature/high‐energy perspective

“…[10]). For comparison, the QMC result of [20] for the Heisenberg model is also displayed. b) At U/t = 8, from single-site DMFT, extrapolations of cluster (DCA) methods, and direct lattice Monte-Carlo (reproduced from [17]).…”