We analyze the internal symmetries and their anomalies in the Kitaev spin-$ S $ models.
Importantly, these models have a lattice version of a $\mathbb {Z} _2 $1-form symmetry …

In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their
generalizations in systems with long-range interactions. We show that, for a quantum spin …

The theory of anyon condensation is the foundation of the bulk-boundary relation and
topological holography in 2+ 1D/1+ 1D. It is believed string condensation should replace …

We compute the mod-2 cohomology ring for three-dimensional (3D) space groups and
establish a connection between them and the lattice structure of crystals with space group …

A bstract We propose the representation principle to study physical systems with a given
symmetry. In the context of symmetry enriched topological orders, we give the appropriate …

Topological phases protected by crystalline symmetries and internal symmetries are shown
to enjoy fascinating one-to-one correspondence in classification. Here we investigate the …

In the study of quantum spin liquids, the Kitaev model plays a pivotal role due to the fact that
its ground state is exactly known as well as the fact that it may be realized in strongly …

Phases with topological order exhibit further complexity in the presence of global
symmetries: States with the same topological order are distinguished by how their anyonic …

Competing interactions in quantum magnets lead to a variety of emergent states, including
ordered phases, nematic magnets and quantum spin liquids. Among them, topological …

In this paper, we study the topological properties of magnons on a dice lattice, also known
as the dual of a more widely studied kagome lattice. This structure has a central atom at the …