Low-dimensional physics of ultracold gases with bound states and the sine-Gordon model

One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how detailed experiments have shown direct evidence for the theoretical treatment of this transition. Then generalization to the case of two-component systems with bound state formation is discussed. Trimer formation in the asymmetric attractive Hubbard model involve in a crucial way this kind of physics