PIRSA:19080085

Computing renormalization invariant properties of Levin-Wen phases

Barter, D. (2019). Computing renormalization invariant properties of Levin-Wen phases. Perimeter Institute. https://pirsa.org/19080085

Barter, Daniel. Computing renormalization invariant properties of Levin-Wen phases. Perimeter Institute, Aug. 22, 2019, https://pirsa.org/19080085 

          @misc{ pirsa_PIRSA:19080085,
            doi = {10.48660/19080085},
            url = {https://pirsa.org/19080085},
            author = {Barter, Daniel},
            keywords = {Mathematical physics},
            language = {en},
            title = {Computing renormalization invariant properties of Levin-Wen phases},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {aug},
            note = {PIRSA:19080085 see, \url{https://pirsa.org}}
          }

Daniel Barter

Australian National University

Talk number
PIRSA:19080085
Collection
Talk Type
Subject
Abstract

 In the 90s Turaev, Viro, Barrett and Westbury constructed a (2+1)D state sum TQFT associated to any fusion category. The associated phases of matter were popularized by Kiteav, Levin and Wen and are now central  examples in condensed matter physics and quantum information theory.

Despite the importance of these phases, many of the computational techniques for working with fusion categories have not percolated into condensed matter physics. Many of these techniques are "folk theorems"
and have not appeared in the literature in a digestible form.

Jacob Bridgeman and myself have spent the last two years extracting these computational techniques from Corey Jones, and have been using them to understand defects in Levin-Wen phases. Our papers 1806.01279,
1810.09469, 1901.08069, 1907.06692 document the development of our understanding, and demonstrate how to do physically relevant fusion category computations.