Finite generalized symmetries in infinite volume

Speaker: Corey Jones (North Carolina State University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

Finite generalized symmetries in one spatial dimension can be described using group actions, (weak) Hopf algebras, or matrix product operators. I will present an operator-algebraic approach in infinite-volume, that starts instead from the symmetric observables: an inclusion B\subseteq A of quasi-local algebras equipped with a conditional expectation. Symmetric states on A correspond exactly to arbitrary states on B, allowing us to study symmetry without committing to a particular realization of symmetry operators. I will explain how this framework recovers the symmetry topological field theory (SymTFT) description and yields classification and realizability results for anyon chains, with connections to rational conformal field theory. I will then introduce an algebra-valued symmetry order parameter that records charge absorption by a state, generalizes familiar group-cohomological indices, and is invariant under symmetric locally generated dynamics