Modified toric code models with flux attachment from Hopf algebra gauge theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909697516240896 |
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| author | Conlon, Mia Pellegrino, Domenico Slingerland, J. K. |
| author_facet | Conlon, Mia Pellegrino, Domenico Slingerland, J. K. |
| contents | 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 finite-dimensional 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 $\mathbb{Z}_{N}$ gauge theory, we find that the introduction of a non-trivial R-matrix amounts to flux attachment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07909 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Modified toric code models with flux attachment from Hopf algebra gauge theory Conlon, Mia Pellegrino, Domenico Slingerland, J. K. Strongly Correlated Electrons Mathematical Physics Quantum Physics 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 finite-dimensional 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 $\mathbb{Z}_{N}$ gauge theory, we find that the introduction of a non-trivial R-matrix amounts to flux attachment. |
| title | Modified toric code models with flux attachment from Hopf algebra gauge theory |
| topic | Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2210.07909 |