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

Dirks, A.; Mikelsons, K.; Krishnamurthy, H.R.; Freericks, J.K.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 89(2): 023306

2014

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.

Related references

**Ultracold atoms in a tunable optical kagome lattice**. Physical Review Letters 108(4): 045305, 2012

**Tonks-Girardeau gas of ultracold atoms in an optical lattice**. Nature 429: 7-81, 2004