Excitations in the higher lattice gauge theory model for topological phases I: Overview
In this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as “higher-lattice gauge theory.” Higher-lattice gauge theory has so-called “2-gau...
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2023
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| _version_ | 1797112517293506560 |
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| author | Huxford, J Simon, S |
| author_facet | Huxford, J Simon, S |
| author_sort | Huxford, J |
| collection | OXFORD |
| description | In this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as “higher-lattice gauge theory.” Higher-lattice gauge theory has so-called “2-gauge fields” describing the parallel transport of lines, in addition to ordinary 1-gauge fields which describe the parallel transport of points. In this series we explicitly construct the creation operators for the pointlike and looplike excitations supported by the model. We use these creation operators to examine the properties of the excitations, including their braiding statistics. These creation operators also reveal that some of the excitations are confined, costing energy to separate that grows linearly with the length of the creation operator used. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to rederive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground-state degeneracy on the 3-torus is related to the number of types of linked looplike excitations. This first paper provides an accessible summary of our findings, with more detailed results and proofs to be presented in the other papers in the series. |
| first_indexed | 2024-03-07T08:26:43Z |
| format | Journal article |
| id | oxford-uuid:c1c4a276-72f6-433e-a94a-36e5711e559f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:26:43Z |
| publishDate | 2023 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:c1c4a276-72f6-433e-a94a-36e5711e559f2024-02-14T12:53:10ZExcitations in the higher lattice gauge theory model for topological phases I: OverviewJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c1c4a276-72f6-433e-a94a-36e5711e559fEnglishSymplectic ElementsAmerican Physical Society2023Huxford, JSimon, SIn this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as “higher-lattice gauge theory.” Higher-lattice gauge theory has so-called “2-gauge fields” describing the parallel transport of lines, in addition to ordinary 1-gauge fields which describe the parallel transport of points. In this series we explicitly construct the creation operators for the pointlike and looplike excitations supported by the model. We use these creation operators to examine the properties of the excitations, including their braiding statistics. These creation operators also reveal that some of the excitations are confined, costing energy to separate that grows linearly with the length of the creation operator used. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to rederive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground-state degeneracy on the 3-torus is related to the number of types of linked looplike excitations. This first paper provides an accessible summary of our findings, with more detailed results and proofs to be presented in the other papers in the series. |
| spellingShingle | Huxford, J Simon, S Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title | Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title_full | Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title_fullStr | Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title_full_unstemmed | Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title_short | Excitations in the higher lattice gauge theory model for topological phases I: Overview |
| title_sort | excitations in the higher lattice gauge theory model for topological phases i overview |
| work_keys_str_mv | AT huxfordj excitationsinthehigherlatticegaugetheorymodelfortopologicalphasesioverview AT simons excitationsinthehigherlatticegaugetheorymodelfortopologicalphasesioverview |