Olesen, Therkel Andreas Zollner; Vlasii, Nadiia Dmytrivna; Wiese, UweJens (2015). From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code. Annals of physics, 361, pp. 303329. Elsevier 10.1016/j.aop.2015.06.020
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We regularize compact and noncompact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the linkpair do not commute. In the noncompact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the linkpair group space R2 in a constant “magnetic” background field. In the compact case, the linkpair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two selfadjoint extension parameters, which form two nondynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a linkpair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)symmetric variant of Kitaev’s toric code, selfadjointly extended by the two nondynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . NonAbelian U(k) Berry gauge fields that arise from the selfadjoint extension parameters may be interesting in the context of quantum information processing.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC) 08 Faculty of Science > Institute of Theoretical Physics 
UniBE Contributor: 
Olesen, Therkel Andreas Zollner; Vlasii, Nadiia Dmytrivna and Wiese, UweJens 
Subjects: 
500 Science > 530 Physics 
ISSN: 
00034916 
Publisher: 
Elsevier 
Language: 
English 
Submitter: 
Esther Fiechter 
Date Deposited: 
10 Sep 2015 15:08 
Last Modified: 
09 Sep 2017 21:47 
Publisher DOI: 
10.1016/j.aop.2015.06.020 
BORIS DOI: 
10.7892/boris.71432 
URI: 
https://boris.unibe.ch/id/eprint/71432 