Conlon, Aaron and Pellegrino, D and Slingerland, J K
(2023)
Modified toric code models with flux attachment from Hopf algebra gauge theory.
Journal of Physics A: Mathematical and Theoretical, 56 (29).
p. 295302.
ISSN 17518121
Abstract
Kitaev’s toric code is constructed using a finite gauge group from gauge theory.
Such gauge theories can be generalized with the gauge group generalized to any finitedimensional semisimple Hopf algebra. This also leads to generalizations of the toric code.
Here we consider the simple case where the gauge group is unchanged but furnished with a
nontrivial quasitriangular structure (Rmatrix), which modifies the construction of the gauge
theory. This leads to some interesting phenomena; for example, the space of functions on
the group becomes a noncommutative algebra. We also obtain simple Hamiltonian models
generalizing the toric code, which are of the same overall topological type as the toric code,
except that the various species of particles created by string operators in the model are
permuted in a way that depends on the Rmatrix. In the case of ZN gauge theory, we find
that the introduction of a nontrivial Rmatrix amounts to flux attachment.
Item Type: 
Article

Keywords: 
Hopf Algebra; Topological lattice models; Gauge Theory; Toric code; 
Academic Unit: 
Faculty of Science and Engineering > Theoretical Physics 
Item ID: 
17815 
Identification Number: 
https://doi.org/10.1088/17518121/acdf9a 
Depositing User: 
IR Editor

Date Deposited: 
10 Nov 2023 12:00 
Journal or Publication Title: 
Journal of Physics A: Mathematical and Theoretical 
Publisher: 
Institute of Physics Publishing Ltd 
Refereed: 
Yes 
URI: 

Use Licence: 
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BYNCSA). Details of this licence are available
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