Title

Tensor networks and categorical Morita invariance

Date

February 12 (Wed), 15:00-16:30, 2025

Place

Room 206 RIMS

Speaker

Christoph Schweigert (Hamburg University)

Abstract

We explain the relation between three-dimensional topological field theories with boundaries and two-dimensional tensor network states. Specifically, we demonstrate how the entries of various tensors, such as Projected Entangled Pair States (PEPS) and Matrix Product Operators (MPO), naturally emerge in the state-sum construction as evaluations of tetrahedral graphs on spheres. These entries are thus (mixed) 6j-symbols, which involve spherical module categories and the associated Morita contexts.

The talk based on work with Jürgen Fuchs, Jutho Haegeman, Laurens Lootens and Frank Verstraete.