Thermal Entropy, Density Disorder, and Antiferromagnetism of Repulsive Fermions in 3D Optical Lattice

The celebrated antiferromagnetic (AFM) phase transition was realized in a most recent optical lattice experiment for the 3D fermionic Hubbard model Shao et al., Nature 632, 267 (2024). Despite this important progress, it was observed that the AFM structure factor (and also the critical entropy) reaches the maximum at an interaction strength U/t ≃ 11.75, which is significantly larger than the theoretical prediction of U/t ≃ 8. Here, we resolve this discrepancy by studying the interplay between the thermal entropy, density disorder, and antiferromagnetism in the halffilled 3D Hubbard model, using numerically exact auxiliary-field quantum Monte Carlo simulations. We have achieved an accurate entropy phase diagram, enabling us to simulate arbitrary entropy path on the temperature-interaction plane and track experimental parameters effectively. We find that above discrepancy can be quantitatively explained by the entropy increase associated with increasing interaction strength in experiment, and together by the lattice density disorder present in the experimental setup. We further investigate the entropy dependence of double occupancy and predict universal behaviors that could serve as valuable probes in future optical lattice experiments.