Publications: Fusion categories

Computing associators of endomorphism fusion categories
with Daniel Barter and Jacob Bridgeman

We present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data, and apply it to compute the associator for the Haagerup fusion category H1.

Journal: SciPost Physics 13, 029 (2022)
ArXiv: 2110.03644

Critical lattice model for a Haagerup conformal field theory
with Robijn Vanhove, Laurens Lootens, Maarten Van Damme, Tobias Osborne, Jutho Haegeman, and Frank Verstraete

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category H3 as input data.

Journal: Physical Review Letters 128, 231602 (2022)
ArXiv: 2110.03532

Generalized string‑nets for unitary fusion categories without tetrahedral symmetry
with Alexander Hahn

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. We present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring the so-called tetrahedral symmetry.

Journal: Physical Review B 102, 115154 (2020)
ArXiv: 2004.07045

Gauging defects in quantum spin systems: A case study
with Jacob Bridgeman, Alexander Hahn, and Tobias J. Osborne

We build a dynamical theory of defects for quantum spin
systems and illustrate it with a spin chain with Vec(Z/2Z) fusion rules.

Journal: Physical Review B 101, 134111 (2020)
ArXiv: 1910.10619

The F-symbols for the H3 fusion category
with Tobias J. Osborne and Deniz E. Stiegemann

We present a solution for the F-symbols of the H3 fusion category, which is Morita equivalent to the even parts of the Haagerup subfactor.

ArXiv: 1906.01322

From categories to anyons: a travelogue
with Kerstin Beer, Dmytro Bondarenko, Alexander Hahn, Maria Kalabakov, Nicole Knust, Laura Niermann, Tobias J. Osborne, Christin Schridde, Stefan Seckmeyer, Deniz E. Stiegemann

We give an introduction into category theory from a physicist’s point of view. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory.

ArXiv: 1811.06670