Microscopic description of 2D topological phases, duality, and 3D state sums
type: Item
instance of: scholarly article
title: Microscopic description of 2D topological phases, duality, and 3D state sums
zbMATH Open document ID: 1201.81099
DOI: 10.1155/2010/671039
published in: Advances in Mathematical Physics
publication date: 2010-11-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0907.3724
review text: Summary: Doubled topological phases introduced by Kitaev, Levin, and Wen supported on two-dimensional lattices are Hamiltonian versions of three-dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum. Equivalence of the previous models in the ground state is shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. An analysis of the ribbon operators describing excitations in both types of models and the three-dimensional geometrical interpretation are given.
Mathematics Subject Classification ID: 81T45
zbMATH DE Number: 5816375
Wikidata QID: Q58650082
author: Zoltan Kadar
author: Annalisa Marzuoli
author: M. Rasetti
MaRDI profile type: Publication
OpenAlex ID: W3100012054
arXiv ID: 0907.3724
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description: scientific article