Speaker: Laurens Lootens (Cambridge)
Title: Matrix product operator symmetries and dualities: theory and applications
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 realised 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 MPOs provide the lattice representation theory of 1D global generalised symmetries. Time permitting, I will discuss several applications of this theory: the classification of duality transformations in (1+1)D, generalised gauging, generalised symmetries as quantum circuits, particle transmission through duality defects, and entanglement structures in gapped phases of matter.