Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …

In (1+ 1)-dimensional topological phases, unpaired Majorana zero modes (MZMs) can arise
only if the internal symmetry group G f of the ground state splits as G f= G b× Z 2 f, where Z 2 …

We study ordinary, zero-form symmetry $ G $ and its anomalies in a system with a one-form
symmetry $\Gamma $. In a theory with one-form symmetry, the action of $ G $ on charged …

We provide a mathematical proposal for the anomaly indicators of symmetries of (2+ 1)-d
fermionic topological orders, and work out the consequences of our proposal in several …

Spatial symmetries can enrich the topological classification of interacting quantum matter
and endow systems with nontrivial strong topological invariants (protected by internal …

In this paper we study gapped boundary states of ZN bosonic symmetry-protected
topological (SPT) phases in (4+ 1) d, which are characterized by mixed ZN-gravity response …

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 …

Abstract Symmetry acting on a (2+ 1) $ D $ topological order can be anomalous in the sense
that they possess an obstruction to being realized as a purely (2+ 1) $ D $ on-site symmetry …

In recent years, fermionic topological phases of quantum matter has attracted a lot of
attention. In a pioneer work by Gu, Wang, and Wen, the concept of equivalence classes of …

Braided-enriched monoidal categories were introduced in the work of Morrison–Penneys,
where they were characterized using braided central functors. The recent work of Kong …