Heidelberg 2022 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 1: Entanglement; Thermalization
MP 1.1: Hauptvortrag
Montag, 21. März 2022, 09:30–10:00, MP-H5
Long-range entanglement and the split property — •Pieter Naaijkens1 and Yoshiko Ogata2 — 1School of Mathematics, Cardiff University, United Kingdom — 2Graduate School of Mathematical Sciences, The University of Tokyo, Japan
Long-range entanglement has been crucial in understanding topologically ordered phases of matter. In particular, it is believed to be a necessary condition for the existence of non-trivial anyons in 2D. In this talk I will explain how we can prove this statement in the context of superselection sector theory. In particular, we show that if a ground state is not long-range entangled, in a way that we make precise, then we only have the trivial superselection sector. I will also indicate how this is related to the split property of certain von Neumann algebras generated by the observables of the system.