DMFT vs Second Order Perturbation Theory for the Trapped 2D Hubbard-Antiferromagnet

In recent literature on trapped ultracold atomic gases, calculations for 2D-systems are often done within the Dynamical Mean Field Theory (DMFT) approximation. In this paper, we compare DMFT to a fully two-dimensional, 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 the order parameter and critical temperatures drastically, spatial fluctuations only play a noticeable role when the system undergoes a phase transition, or at phase boundaries in the trap. We conclude from this that DMFT is a good approximation for the antiferromagnetic Fermi-Hubbard model for experimentally relevant system sizes.