IAS CMT/QFT Group Meeting

Abstract: A decade of work in band theory has built towards an understanding of topology that is largely based on the character theory of the space group. The (thousands of) topological materials predicted in this way provide a diverse set of symmetry-protected topological phases (SPTs), anticipating a complete classification. Attempts so far are typically axiomatic and based on group cohomology. In this talk, I will present an elementary approach to the problem that is motivated by (but departs from) the non-interacting classification produced by band theory. I will define many-body trivial, fragile topological, and stable topological phases which are accompanied by explicit topological indices. These indices can be simply interpreted as local Noether charges protected by the space group. I will argue that they are the coefficients of Wen-Zee terms in the topological quantum field theory describing the SPT. They form a dictionary between field theory and materials chemistry.