Speaker
David Perez Garcia, Universidad Complutense de Madrid
Abstract
Haag duality is a strong notion of locality for two-dimensional quantum spin systems. Originally introduced by Rudolf Haag in the 1950s within the framework of algebraic quantum field theory, it has recently become pivotal to the operator-algebraic analysis of topological quantum many-body systems. Until now, Haag duality had only been proven for Kitaev’s quantum double models based on Abelian groups. In this talk, we will show that Haag duality holds for representatives of all known 2D non-chiral quantum phases of matter. In conjunction with the stability under quasilocal automorphisms of a weaker version, called approximate Haag duality, we conclude that all states within all known phases exhibit approximate Haag duality. The proof is based on an operator-algebraic reduction of the Haag duality condition to finite systems, which we verify using tensor-network techniques.
(Joint work with Yoshiko Ogata and Alberto Ruiz de Alarcon)