Dynamical mean-field theory versus second-order perturbation theory for the trapped two-dimensional Hubbard antiferromagnet

In recent literature on trapped ultracold atomic gases, calculations for two-dimensional (2D) systems are often done within the dynamical mean-field theory (DMFT) approximation. In this paper, we compare DMFT to a fully 2D, self-consistent second-order perturbation theory for weak interactions in a repulsive Fermi-Hubbard model. We investigate the role of quantum and of spatial fluctuations when the system is in the antiferromagnetic phase, and find that, while quantum fluctuations decrease drastically the order parameter and critical temperatures, spatial fluctuations only play a noticeable role when the system undergoes a phase transition, or at phase boundaries in the trap. We conclude f…