# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 35: Poster 2

### Q 35.7: Poster

### Mittwoch, 14. März 2012, 16:30–19:00, Poster.I+II

**Quasi-particle Theory of strongly correlated Lattice Bosons - Application to the Bose-Hubbard Model** — •Michael Buchhold, Ulf Bissbort, and Walter Hofstetter — Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, D-60438 Frankfurt/Main, Germany

We present a quasi-particle theory for strongly interacting lattice bosons, which, in contrast to Bogoliubov theory, is also valid for strong depletion of the condensate and in the Mott insulating phase. The derivation is based on the linearization of the equations of motion for a Gutzwiller variational state and a quantization of the classical amplitudes of the resultant excitations.

Within this theory of non-interacting quasi-particles, we calculate the single-particle spectral function of the single-band Bose-Hubbard model. In addition to the gapless Bogoliubov mode, we also clearly resolve the amplitude mode, which becomes particularly relevant in the strongly correlated regime, in the vicinity of the superfluid-Mott transition. Subsequently we express physical operators in terms of quasi-particles, which directly reveals the coupling to the system’s eigenmodes. In particular, we demonstrate this for the Bragg operator in lattice representation.

Our first application beyond theories of non-interacting quasi-particles is to take higher order terms into account which we initially neglected in the derivation. We determine the quasi-particle lifetimes as well as the induced broadening of the spectral function.