Repositorio
Institucional

de Resende, M. F. Araujo

Jimenez, J. P. Ibieta

Espiro, J. Lorca

Quantum double models coupled to matter fields: A detailed review for a dualization procedure

WORLD SCIENTIFIC PUBL CO PTE LTD

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION

en

In this paper, we investigate how it is possible to define a new class of lattice gauge models based on a dualization procedure of a previous generalization of the Kitaev Quantum Double Models. In the case of this previous generalization that will be used as a basis, it was defined by adding new qudits (which were denoted as matter fields in reference to some works) to the lattice vertices with the intention of, for instance, interpreting its models as Kitaev Quantum Double Models coupled with Potts ones. Now, with regard to the generalization that we investigate here, which we want to define as the dual of this previous one, these new qudits were added to the lattice faces. And as the coupling between gauge and matter qudits of the previous generalization was performed by a gauge group action, we show that the dual behavior of these two generalizations was achieved by coupling these same qudits in the second one through a gauge group co-action homomorphism. One of the most striking dual aspects of these two generalizations is that, in both, part of the quasiparticles that were inherited from the Kitaev Quantum Double Models become confined when these action and co-action are nontrivial. But the big news here is that, in addition to the group homomorphism (that defines this gauge group co-action) allows us to classify all the different models of this second generalization, this same group homomorphism also suggests that all these models can be interpreted as two-dimensional restrictions of the 2-lattice gauge theories.

2023

artículo de revisión

10.1142/S0219749923500181

PDF

Quantum double models

lattice gauge theories

confinement properties

topological order

algebraic order

Ciencias de la Computación

Física

Modelos dobles cuánticos

teorías de calibre de red

propiedades de confinamiento

orden topológico

orden algebraico

artículo de revisión

versión publicada

metadata

https://arxiv.org/pdf/1904.02153

metadata

WOS:000974893000001

0219-7499

verde

Ciencias de la Computación

Física

CNPq 162117/2015-9