Topological quantum computation has emerged as one of the most exciting approaches to
constructing a fault-tolerant quantum computer. The proposal relies on the existence of …

Monoidal category theory serves as a powerful framework for describing logical aspects of
quantum theory, giving an abstract language for parallel and sequential composition, and a …

A bstract In general quantum field theories (QFTs), ordinary (0-form) global symmetries and
1-form symmetries can combine into 2-group global symmetries. We describe this …

We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

A bstract We classify all non-invertible Kramers-Wannier duality defects in the E 8 lattice
Vertex Operator Algebra (ie the chiral (E 8) 1 WZW model) coming from ℤ m symmetries. We …

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio
is not an integer! But this can happen for generalizations of vector spaces—objects of a …

A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest
neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of …

We study 3d and 4d systems with a one-form global symmetry, explore their consequences,
and analyze their gauging. For simplicity, we focus on $\mathbb {Z} _N $ one-form …

Let K be a commutative ring with unit. For a K-linear endomorphism f: X! X of a free K-
module of ˇnite rank X, we have the usual trace Tr (f) 2 K deˇned as the trace of the matrix of f …

We construct topological defects in two-dimensional classical lattice models and quantum
chains. The defects satisfy local commutation relations guaranteeing that the partition …