Darmstadt 2008 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 15: Quantengase (Gitter I)
Q 15.5: Vortrag
Dienstag, 11. März 2008, 15:00–15:15, 1C
Diagrammatic Calculation of Finite-Temperature Properties of the Bose-Hubbard Model — Henrik Enoksen1, Alexander Hoffmann2, •Matthias Ohliger3, and Axel Pelster4 — 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway — 2Arnold Sommerfeld Center for Theoretical Physics, Theresienstr. 37, Department Physik, Universität München, 80333 München, Germany — 3Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany — 4Fachbereich Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
Following an approach first worked out by Metzner in the context of electrons in conductors [1], we use a diagrammatic hopping expansion to calculate finite-temperature Green’s functions for the Bose-Hubbard model which describes bosons in an optical lattice. This allows us to reconstruct in a qualitative way the time-of-flight absorption pictures, which are taken after the optical lattice is switched off. Furthermore, the technique makes summations of subsets of diagrams possible, leading to non-perturbative results for locating the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by Monte-Carlo simulations of the Bose-Hubbard model.
[1] W. Metzner, Phys. Rev. B 43, 8549 (1993)