title: Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory.
abstract: We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) × 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.
authors.affiliation: Department of Physics, Georgetown University, Washington, DC 20057, USA.
authors.forename: Andreas
authors.initials: A
authors.lastname: Dirks
authors.affiliation: Department of Physics, Georgetown University, Washington, DC 20057, USA.
authors.forename: Karlis
authors.initials: K
authors.lastname: Mikelsons
authors.affiliation: Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India and Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India.
authors.forename: H R
authors.initials: HR
authors.lastname: Krishnamurthy
authors.affiliation: Department of Physics, Georgetown University, Washington, DC 20057, USA.
authors.forename: James K
authors.initials: JK
authors.lastname: Freericks