Critical Entropy of Quantum Heisenberg Magnets on Simple-Cubic Lattices

TL;DR

This study investigates the entropy behavior at the critical temperature of quantum Heisenberg magnets on cubic lattices using advanced Monte Carlo simulations, providing key entropy values for both antiferromagnetic and ferromagnetic cases.

Contribution

It introduces optimized extended ensemble quantum Monte Carlo methods to accurately determine the critical entropy of 3D Heisenberg models, comparing results with experimental proposals.

Findings

Critical entropy density for antiferromagnetic case: 0.341(5)$k_B$

Critical entropy density for ferromagnetic case: 0.401(5)$k_B$

Results relevant for ultra-cold fermion gas experiments

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)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic N\'eel state in ultra-cold fermion gases in optical lattices.