Abstract

The accurate simulation of fermionic quantum many body problems is one of the most important challenges in theoretical physics, with huge impact especially on the understanding and design of materials. However, the exponential scaling of the Hilbert space make direct simulations impossible for all but the smallest systems and Monte Carlo simulations suffer from the negative sign problem. The goal thus has to be to develop efficient approximate methods for fermionic systems. I will report on recent progress in the simulation of fermionic systems, especially in the context of ultracold atomic gases in optical lattices. In deep optical lattice fermionic gases are well described by the Hubbard model, which we can now accurately simulate down to the Néel temperature, substantially lower than the lowest temperature achieved in experiments so far. In shallow optical lattices the simulation and the physics become more complex, as band mixing and orbital effects become important, and multi-band models are hard to derive and simulate. Here we propose to use density functional theory for such systems, using a new exchange correlation functional for ultracold atomic gases instead of electrons. This lets us use all the tools developed for materials simulations also for the simulation of atomic gases. In the future, comparison to controlled experiments will allow to test and improve density functionals for strongly correlated fermionic systems, and thus in return also improve simulation methods for materials.