PIRSA:26020054

Matrix Product Operator Symmetries: Theory and Applications

Lootens, L. (2026). Matrix Product Operator Symmetries: Theory and Applications. Perimeter Institute. https://pirsa.org/26020054

Lootens, Laurens. Matrix Product Operator Symmetries: Theory and Applications. Perimeter Institute, Feb. 27, 2026, https://pirsa.org/26020054 

          @misc{ pirsa_PIRSA:26020054,
            doi = {10.48660/26020054},
            url = {https://pirsa.org/26020054},
            author = {Lootens, Laurens},
            keywords = {Mathematical physics},
            language = {en},
            title = {Matrix Product Operator Symmetries: Theory and Applications},
            publisher = {Perimeter Institute},
            year = {2026},
            month = {feb},
            note = {PIRSA:26020054 see, \url{https://pirsa.org}}
          }

Laurens Lootens University of Cambridge

Talk numberPIRSA:26020054
DOI10.48660/26020054
Collection
Talk Type Scientific Series
Subject

Abstract

In recent years, non-onsite symmetry representations on the
lattice have enabled new insights in both anomalous and non-invertible
symmetries.  In (1+1)D, these can be represented as matrix product
operators (MPO), a type of tensor network that captures the correlated
action on neighbouring sites.  In this talk, I will present the
underlying mathematical structures that govern these symmetries, and
show that these MPOs provide the lattice representation theory of
generalised symmetries in (1+1)D.  Time permitting, I will discuss some
applications of these ideas, in particular how they can be leveraged to
improve computational performance in state of the art in tensor network
algorithms.

Based on arXiv:2509.03600, arXiv:2408.06334