Laboratoire de Physique Théorique
Toulouse - UMR 5152

Topological phases exist beyond the standard Ginzburg-Landau paradigm that dominated the understanding of phases and phase transitions in condensed matter systems. Paradigmatic examples have been derived to establish a new theoretical basis that takes into consideration these topological aspects. The spin 1 Haldane phase is one of them for the unidimensional case. The seminar presents a way to implement this phase as well as its suggested generalizations by focusing using ultracold fermionic alkaline-earth atoms, that involve an internal SU($N$) symmetry. The model describing the experiment is called the double-well model and depicts a lattice of two interacting chains. The model is analysed at weak coupling, strong coupling and using a numerical tool : DMRG.