We review some numerical works carried out within the department for Quantum
Optics and Statistics at the University of Freiburg’s Institute of Physics, between
September 2016 and June 2018. Our activities focus on quantum properties of
matter at zero temperature, i.e., a regime where the thermal energy kBT is negligible
with respect to the other energy scales of the considered system. This
area of research, related to ultracold gases, has attracted a great deal of interest,
both experimentally and theoretically, since the first realization of a Bose-Einstein
condensate in 1995. In a context where the theoretical understanding of these
systems still remains challenging, the growing power of computers offers a unique
and efficient way to tackle such challenges. In our theory group, we particularly
use powerful numerical methods that give exact results, in contrast to other theoretical
approaches based on an a priori assumption, e.g., mean field theory. To
illustrate it, we focus on few typical results that would not be available other
than by using high performance computing. These results have been obtained by
using three numerical methods: quantum Monte Carlo (QMC), Gutzwiller Monte
Carlo (GMC), and the Multiconfigurational Time-dependent Hartree method for
bosons (MCTDHX)
