Matrix Product States in the Continuum and Cold Atomic Gases

Cold atomic gases are an ideal laboratory to explore the physics of interacting degenerate quantum gases due to the high degree of tunability possible in the experiments. In particular, special trapping arrangements allow, among other things, to control the effective dimensionality of the systems. In this talk we present an update on the continuum formulation of Matrix Product States (cMPS) to describe one dimensional dilute quantum gases. The goal is to develop cMPS as an accurate predictive tool to plan and analyse past and future experiments. To that end, we shall present results for the cases of trapped single-species and multi-species bosonic and fermionic atoms, as well as their mixtures. When available, we make quantitative comparisons of cMPS results with the exact results for solvable cases.