Didier Poilblanc : Topological order in Condensed Matter and beyond (IRSAMC 3 décembre 2018)

Didier Poilblanc
Laboratoire de Physique Théorique (LPT), Toulouse

LIEU  : Salle 20, RDC bâtiment 3R1B4- Bat. IIIr1-B4
DATE  : lundi 3 décembre à 14h

Most quantum phases of matter (magnetic phases, superconductivity, etc…) can be described within the unified Ginzburg-Landau (GL) framework formalizing the concept of spontaneous symmetry breaking (e.g. spin rotation symmetry is spontaneously broken in a quantum antiferromagnet).

However, tremendous interest has grown recently for so-called "topological phases of matter", due to their potential to host exotic "anyonic" particles with "fractional" statistics, the fundamental bricks of the proposed (A. Kitaev 2005) revolutionary "topological quantum computer". Such amazing quantum states cannot be described within the GL paradigm (for example they do not exhibits symmetry breaking neither do they have a local order parameter), but rather, are characterized by the new emerging concept of "topological order" (X.G. Wen 1990) or "long range entanglement"(LRE). Besides bulk anyonic excitations, "chiral" topological phases also exhibit chiral edge modes protected by LRE.

Fractional Quantum Hall states (FQHS), realized by (ultra-pure) interacting electrons in the plane on the presence of a magnetic field, fall into such a category. I will discuss the discovery of "chiral spin liquids" which can be viewed as the (2D) lattice quantum spin analogs of the FQHS. CSL can be realized in Condensed Matter materials or in systems of Ultracold atoms on optical lattices. I will also show that new theoretical tools such as "Tensor networks", borrowed from the field of quantum information, are necessary to obtain a proper description/understanding of such topological phases.

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