Enforced symmetry breaking by invertible topological order

Abstract

It is well known that two-dimensional Chern insulator must break the time reversal symmetry, as manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topological order and symmetry can occur more generally. In this talk, I will discuss enforced breaking of general discrete internal symmetries by a class of fermionic topological orders, namely invertible topological orders. General criteria and examples will be discussed for 0D, 1D and 2D systems. These results rely on a general exploration of symmetry-enriched invertible topological orders and quantum anomaly.