M. Aizenman, E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
Preprint series: ESI preprints

MSC:

81V70 Many-body theory

Abstract: One of the most remarkable recent developments in the study of
ultracold Bose gases is the observation of a reversible transition
from a Bose Einstein condensate to a state composed of localized
atoms as the strength of a periodic, optical trapping potential is
varied. In \cite{ALSSY} a model of this phenomenon has been analyzed
rigorously. The gas is a hard core lattice gas and the optical
lattice is modeled by a periodic potential of strength $\lambda$.
For small $\lambda$ and temperature Bose-Einstein condensation (BEC)
is proved to occur, while at large $\lambda$ BEC disappears, even in
the ground state, which is a Mott-insulator state with a
characteristic gap. The inter-particle interaction is essential for
this effect. This contribution gives a pedagogical survey of these
results.