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 10d×10d 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.
- Publication:
-
Physical Review E
- Pub Date:
- February 2014
- DOI:
- 10.1103/PhysRevE.89.023306
- arXiv:
- arXiv:1309.5994
- Bibcode:
- 2014PhRvE..89b3306D
- Keywords:
-
- 02.60.Nm;
- 03.75.Ss;
- 71.10.Fd;
- Integral and integrodifferential equations;
- Degenerate Fermi gases;
- Lattice fermion models;
- Condensed Matter - Strongly Correlated Electrons;
- Condensed Matter - Quantum Gases
- E-Print:
- 14 pages, 9 figures