Résumé : Abstract: Exotic types of order that go beyond Landau’s theory of spontaneous symmetry breaking continue to captivate the attention of condensed matter physicists. Using the language of spins often allows for construction of models that are analytically and/or numerically tractable, yet still highly relevant to experiments. In the recent years, much progress has been made in one and two dimensions, which are particularly well-suited for a theoretical study. However, there are two indisputable reasons to go beyond 2D: firstly, most of the compounds surrounding us are, in fact, three dimensional. Second, but no less important, reason is that higher dimensions give rise to even richer and more exotic physical phenomena. One of the examples of exotic quantum order is the so-called topological phases. Originally proposed in two dimensions, topological phases have ground state degeneracies that depend solely on the topology that the system is embedded in. This topological degeneracy of the ground state is directly linked to the existence of gapped excitations, termed anyons, whose exchange statistics are strikingly different from the familiar bosons and fermions. Pointlike anyons can only exist in two-dimensions, however the concept of topological order has been extended beyond 2D via two main avenues: (a) introducing extended (e.g., loop-like) anyon excitations, and (b) fracton topological order. The latter phases host pointlike excitations that are immobile: strictly localized in space. In my talk, I will introduce a simple toy model with this type of order, starting from a layered construction of two-dimensional toric codes.
Lieu : salle 208a, aîle sud LPS, bât 510