Promotionsvortrag Physik: „Quantum lattice models with long-range interactions — quantum phase transitions and crystalline ground states“

Ankündigung des Promotionsvortrags von: Herrn Jan Koziol

In the cumulative thesis, we discuss the low-energy properties of quantum lattice models with algebraically decaying long-range interactions.

A large portion of the publications included in the thesis is based on the unit-cell-based optimiza-tion scheme, which will be the main focus of this talk.

The method enables the systematic search for periodic ground states in lattice models with long-range interactions in the thermodynamic limit without any truncation of the interaction.

It is based on the observation that one can evaluate the energy of a periodic state in the thermo-dynamic limit, considering solely a model on its unit cell with appropriately resummed couplings.

The idea is to invert the reasoning and formulate the ground-state search as an optimization prob-lem of these resummed models on all unit cells of interest.

This provides ground-state estimates for classical (diagonal) lattice problems with long-range in-teractions limited only by the sizes of the considered unit cells and the optimization procedures used on each one of them.

We further extend this scheme to the treatment of quantum lattice problems in a mean-field ap-proximation.

With this method, we discuss the melting of devil's staircases of crystalline phases against quan-tum fluctuations: (i) a nearest-neighbour hopping and (ii) a linear coupling to a single bosonic mode.

In both cases, we find states in the phase diagram that are stabilized by the interplay of quantum fluctuations and long-range interactions.

(Vortrag auf Englisch)

Dem Vortrag schließt sich eine Diskussion von 15 Minuten an. Vortrag und Diskussion sind öffentlich. Diesen Verfahrensteilen folgt ein nicht öffentliches Rigorosum von 45 Minuten.