From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code
Data(s) |
08/07/2015
31/12/1969
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Resumo |
We regularize compact and non-compact 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 link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair 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 self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair 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, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing. |
Formato |
application/pdf application/pdf |
Identificador |
http://boris.unibe.ch/71432/1/1-s2.0-S0003491615002651-main.pdf http://boris.unibe.ch/71432/8/From%20Doubled%20Chern-Simons-Maxwell%20Lattice.pdf Olesen, Therkel Andreas Zollner; Vlasii, Nadiia Dmytrivna; Wiese, Uwe-Jens (2015). From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code. Annals of physics, 361, pp. 303-329. Elsevier 10.1016/j.aop.2015.06.020 <http://dx.doi.org/10.1016/j.aop.2015.06.020> doi:10.7892/boris.71432 info:doi:10.1016/j.aop.2015.06.020 urn:issn:0003-4916 |
Idioma(s) |
eng |
Publicador |
Elsevier |
Relação |
http://boris.unibe.ch/71432/ |
Direitos |
info:eu-repo/semantics/restrictedAccess info:eu-repo/semantics/openAccess |
Fonte |
Olesen, Therkel Andreas Zollner; Vlasii, Nadiia Dmytrivna; Wiese, Uwe-Jens (2015). From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code. Annals of physics, 361, pp. 303-329. Elsevier 10.1016/j.aop.2015.06.020 <http://dx.doi.org/10.1016/j.aop.2015.06.020> |
Palavras-Chave | #530 Physics |
Tipo |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion PeerReviewed |