Quantum Monte Carlo simulations of antiferromagnetism in ultracold fermions on optical lattices within real-space dynamical mean-field theory

We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary mixture of repulsively interacting fermionic atoms harmonically trapped in an optical lattice. We explore temperature effects and establish signatures of the N'{e}el transition in observables directly accessible in cold-atom experiments; entropy estimates are also provided. We demonstrate that the local density approximation (LDA) fails for ordered phases. In contrast, a “slab” approximation allows us to reach experimental system sizes with O(10^5) atoms without significant loss of accuracy.