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We present a nonequilibrium strong-coupling approach to inhomogeneous systemsof ultracold atoms in optical lattices. We demonstrate its application to theMott-insulating phase of a two-dimensional Fermi-Hubbard model in the presenceof a trap potential. Since the theory is formulated self-consistently, thenumerical implementation relies on a massively parallel evaluation of theself-energy and the Green's function at each lattice site, employing thousandsof CPUs. While the computation of the self-energy is straightforward toparallelize, the evaluation of the Green's function requires the inversion of alarge sparse $10^d\times 10^d$ matrix, with $d > 6$. As a crucial ingredient,our solution heavily relies on the smallness of the hopping as compared to theinteraction strength and yields a widely scalable realization of a rapidlyconverging iterative algorithm which evaluates all elements of the Green'sfunction. Results are validated by comparing with the homogeneous case via thelocal-density approximation. These calculations also show that thelocal-density approximation is valid in non-equilibrium setups without masstransport.

physical review. e, statistical, nonlinear and soft matter physics

Simulation of inhomogeneous distributions of ultracold atoms in an  optical lattice via a massively parallel implementation of nonequilibrium  strong-coupling perturbation theory