Title: The higher dimensional algebra of matrix product operators and quantum spin chains

Date: 09/26/2019

Time: 11:30 AM - 12:30 PM

Place: C304 Wells Hall

In the context of 1D quantum spin chains, matrix product operators provide a way to study non-local operators such as translation in terms of quasi-local information. They have been used to describe a generalized form of symmetry for 1D systems on the boundary of 2D topological phases. In this talk, we will introduce some concepts of higher dimensional algebra, and a broad hypotheses about higher categories and spatially extended quantum systems. We will then explain how the collection of matrix product operators assembles into a higher (symmetric monoidal 2-) category, and discuss some implications of this. Based on joint work with David Penneys.