The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–
Anderson–Higgs mechanism, ie, after a spontaneous symmetry breaking, a bosonic field …

A large class of gapped phases of matter can be described by topological finite group gauge
theories. In this paper, we show how such gauge theories possess a higher-group global …

We provide a classification of invertible topological phases of interacting fermions with
symmetry in two spatial dimensions for general fermionic symmetry groups G f and general …

D topological phases of matter can host a broad class of non-trivial topological defects of
codimension-1, 2, and 3, of which the well-known point charges and flux loops are special …

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 the presence of crystalline symmetries, topological phases of matter acquire a host of
invariants leading to nontrivial quantized responses. Here we study a particular invariant …

We show how to define a quantized many-body charge polarization 𝒫→ for (2+ 1) D
topological phases of matter, even in the presence of nonzero Chern number and magnetic …

While free fermion topological crystalline insulators have been largely classified, the
analogous problem in the strongly interacting case has been only partially solved, and the …

The Kähler-Dirac fermion, recognized as an elegant geometric approach, offers an
alternative to traditional representations of relativistic fermions. Recent studies have …

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 …