Numerical Investigation of Strongly Interacting Bosons at Zero Temperature

Abstract

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).