From DHR Sectors to DHR Bimodules: Superselection Theory for Infinite Quantum Spin Chains

Traditional descriptions of internal symmetry begin with a field algebra, a symmetry group, and a Hilbert-space representation. The observable algebra is then obtained as the fixed-point algebra, and the Hilbert space decomposes into charge sectors associated with irreducible representations of the symmetry group. In contrast, DHR superselection theory adopts a bottom-up perspective: it starts from the net of local observable algebras and describes charges as localized and transportable representations that agree with the vacuum representation outside bounded regions.For infinite quantum lattice systems, the usual representation-theoretic formulation remains dependent on a distinguished ground-state representation. DHR bimodule theory replaces states by unital completely positive maps and Hilbert-space representations by bimodule. Applied to the identity channel of the quasi-local algebra, this construction produces a canonical, state-independent C*-tensor category of localizable bimodules. In this talk, I will review the basic structure of DHR theory, introduce DHR bimodules and their localization condition, and explain the role of weak algebraic Haag duality in constructing a braiding. I will conclude with fusion spin chains associated with a unitary fusion category, whose DHR bimodule category is braided equivalent to the Drinfeld center.