Hannover 2013 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 40: Quantum gases: Optical lattices II

Q 40.5: Vortrag

Mittwoch, 20. März 2013, 15:00–15:15, A 310

An Efficient Approach to Calculating Wannier States and Extension to Inhomogeneous Systems — •Ulf Bissbort and Walter Hofstetter — ITP, Goethe-Universität Frankfurt

Wannier states are a fundamental and central constituent to the construction of many-body models, as they are restricted to the single-particle Hilbert subspace of the respective band, while minimizing the spatial spread. Although simple in their initial definition as discrete Fourier transforms of the Bloch states, their actual computation amounts to a non-trivial high-dimensional minimization problem of the spatial variance as a complex phases of the single-particle Bloch state. Various involved techniques have been devised to efficiently treat this minimization problem, which quickly becomes numerically demanding for all but the simplest lattice geometries. We present an alternative approach, which allows for an efficient numerical calculation of the maximally localized Wannier states and entirely circumvents the pitfalls associated with the minimization technique, such as getting stuck in local minima. The computational effort scales favorably with increasing dimensions and lattice geometries in comparison to the minimization technique. Furthermore it allows for the first clear and unambiguous definition of Wannier states in inhomogeneous systems.