David Perez-Garcia: Haag duality for 2D quantum spin systems

Speaker
David Perez-Garcia, Universidad Complutense de Madrid

Abstract
Haag duality is a fundamental locality property introduced in the pioneering formulation of algebraic quantum field theory by Haag and Kastler in the 1960s. Since then, it has played a central role, most notably in the classification of superselection sectors by Doplicher, Haag, and Roberts in the 1970s. Over the past two decades, this concept has migrated from its relativistic origins to quantum spin systems, becoming a cornerstone of the operator-algebraic approach to the long-standing problem of classifying two-dimensional topological quantum phases of matter. However, rigorous proofs of Haag duality in two dimensions were previously restricted to systems exhibiting abelian anyons. In this talk, we will establish Haag duality for a broad class of tensor network models, expected to include representatives of all non-chiral topological quantum phases of matter.