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 1751-8121

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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 non-trivial quasitriangular structure (R-matrix), 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 non-commutative 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 R-matrix. In the case of ZN gauge theory, we find that the introduction of a non-trivial R-matrix 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/10.1088/1751-8121/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:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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