Haag duality for Kitaev's quantum double model for abelian groups

Naaijkens, Pieter ORCID: https://orcid.org/0000-0001-5670-243X and Fiedler, Leander 2015. Haag duality for Kitaev's quantum double model for abelian groups. Reviews in Mathematical Physics 27 (09) , 1550021. 10.1142/S0129055X1550021X

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Abstract

We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localised outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localised in disjoint regions commute.As an application we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	World Scientific Publishing
ISSN:	0129-055X
Date of First Compliant Deposit:	23 March 2020
Date of Acceptance:	18 October 2015
Last Modified:	24 Nov 2024 01:30
URI:	https://orca.cardiff.ac.uk/id/eprint/129632

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