Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Localized endomorphisms in Kitaev's toric code on the plane

Naaijkens, Pieter 2011. Localized endomorphisms in Kitaev's toric code on the plane. Reviews in Mathematical Physics 23 (04) , p. 347. 10.1142/S0129055X1100431X

Full text not available from this repository.

Abstract

We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized endomorphisms of the observable algebra. The structure of these endomorphisms is analyzed in the spirit of the Doplicher–Haag–Roberts program (specifically, through its generalization to infinite regions as considered by Buchholz and Fredenhagen). Most notably, the statistics of excitations can be calculated in this way. The excitations can equivalently be described by the representation theory of , i.e. Drinfel'd's quantum double of the group algebra of ℤ2.

Item Type: Article
Status: Published
Schools: Mathematics
Publisher: World Scientific Publishing
ISSN: 0129-055X
Last Modified: 14 Feb 2020 16:45
URI: http://orca.cf.ac.uk/id/eprint/129629

Citation Data

Cited 16 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item