Dresden 2011 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 46: Ultra-cold atoms, ions and BEC V

Q 46.3: Vortrag

Donnerstag, 17. März 2011, 11:00–11:15, BAR 106

Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods — •Christina Kraus and Ignacio Cirac — Max-Planck Institut für Quantenoptik, Garching

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to the Fermionic Gaussian state that optimally approximates the quantum state of the fermions. The methods apply to relatively large systems, since their complexity only scales quadratically with the number of lattice sites. Moreover, they are specially suited to describe inhomogenous systems, as those typically found in recent experiments with atoms in optical lattices, at least in the weak interaction regime. As a benchmark, we have applied them to the two-dimensional Hubbard model on a 10x10 lattice with and without an external confinement.