Tessellation and constellations in the hyperbolic plane and applications to topolo...
De Sitter special relativity: foundations and physical applications
| Full text | |
| Author(s): |
Padmanabhan, Pramod
;
Ibieta-Jimenez, Juan Pablo
;
Bernabe Ferreira, Miguel Jorge
;
Teotonio-Sobrinho, Paulo
Total Authors: 4
|
| Document type: | Journal article |
| Source: | ANNALS OF PHYSICS; v. 372, p. 238-259, SEP 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models. which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Z(n) and S-3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z(2) phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties. (C) 2016 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 12/21355-9 - Gauge Theories and Topological models |
| Grantee: | Miguel Jorge Bernabé Ferreira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |