Etude des phases topologiques de type Haldane par l'intermédiaire d'un système de fermions alcalno-terreux ultrafroids de type double-puits

Abstract : Topological phases exist beyond the standard Ginzburg-Landau paradigmthat 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 present thesis aims to study this phase as well as its suggested generalizations by focusing on a way to implement them experimentally 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. At half-filling and inthe regime of srong repulsions between particles in the same well as well as two facing wells, a Haldane-like symmetry-protected topological phase is systematically expected for all N, including the "chiral" Haldane phase. The effective model obtained when N Æ 3 is the 3-3bar ladder model (describing two spin chains, one in the fondamental representation of SU(N), and the other in its conjuguate) and is particulary explored.
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Pierre Fromholz. Etude des phases topologiques de type Haldane par l'intermédiaire d'un système de fermions alcalno-terreux ultrafroids de type double-puits. Physique [physics]. Université de Cergy Pontoise, 2018. Français. ⟨NNT : 2018CERG0976⟩. ⟨tel-02286006⟩

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