Symmetry, Topology, and Quantum Phases of Matter: From Tensor Networks to Physical Realizations

Coordinators: Ignacio Cirac, Lukasz Fidkowski, Ashvin Vishwanath, and Cenke Xu

The theoretical discovery of topological insulators (TIs) highlighted the deep interplay between symmetry and topology in quantum phases of matter. The experimental realization of TIs in a host of real materials has indicated that topological phenomena are more common in nature than previously anticipated. Encouraged by these developments, theory has made rapid progress in the understanding of general interacting phases that can realize such phenomena. This includes the discovery of effects available only to strongly interacting systems, of modifications to the free fermion classification of TIs, and of constraints on the symmetry properties of spin liquids. The methods employed include ideas from quantum information theory and advanced mathematical techniques from algebra and topology. However, much work remains to be done to tie together these disparate approaches, and more importantly to connect them to realistic models that can be examined numerically and realized in nature.

This program will bring together theorists, computational physicists, and experimentalists to tackle these issues. Some specific goals and questions to be addressed by this program are 1) What is the classi�cation of topological and symmetry protected phases, and what are the robust detectable signatures of the different phases? 2) Are there inherently strongly interacting analogues of topological insulators, and can they be realized in strongly correlated materials like SmB6? 3) Can numerical methods like tensor networks be useful in modeling these phases?

There will be an associated conference, to be held October 17-21, 2016.