Abstract
It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking by topological orders. In this work, we systematically study enforced breaking of a general finite group Gf by a class of topological orders, namely 0D, 1D and 2D fermionic invertible topological orders. In this talk, we will discuss a series of criteria on the existence or non-existence of enforced symmetry breaking by the fermionic invertible topological orders. Using these criteria, we discover many examples that are not known previously. We also study enforced breaking of some continuous group by 2D invertible topological orders through a different argument. For 2D systems, we define the physical quantities to describe symmetry- enriched invertible topological orders and derive some obstruction functions using both fermionic and bosonic languages. In the latter case which is done via gauging the fermion parity, we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system.
Biography
Shangqiang Ning is now a post-doctoral fellow at the Department of physics of The Chinese University of Hong Kong. He received his BS degree at Shandong University in 2014, and then move to Tsinghua University where he received his PhD degree in 2019. He was the post-doctoral fellow from Sept, 2019 to Sept, 2021 at the Department of Physics in The University of Hong Kong. His research area focus on the symmetry and topology in strongly correlated condensed matter systems.
Anyone interested is welcome to attend.