Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909103681437696 |
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| author | Huxford, Joe Simon, Steven H. |
| author_facet | Huxford, Joe Simon, Steven H. |
| contents | In this work, the second paper of this series, we study the 2+1d version of a Hamiltonian model for topological phases based on higher lattice gauge theory. We construct the ribbon operators that produce the point-like excitations. These ribbon operators are used to find the braiding properties and topological charge carried by the point-like excitations. The model also hosts loop-like excitations, which are produced by membrane operators. By considering a change of basis, we show that, in certain cases, some loop-like excitations represent domain walls between patches corresponding to different symmetry-related ground states, and we find this symmetry. We also map the higher lattice gauge theory Hamiltonian to the symmetry enriched string-net model for symmetry enriched topological phases (SETs) described by Heinrich, Burnell, Fidkowski and Levin [Phys. Rev. B, 94, 235136 (2016)], again in a subset of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05341 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case Huxford, Joe Simon, Steven H. Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics In this work, the second paper of this series, we study the 2+1d version of a Hamiltonian model for topological phases based on higher lattice gauge theory. We construct the ribbon operators that produce the point-like excitations. These ribbon operators are used to find the braiding properties and topological charge carried by the point-like excitations. The model also hosts loop-like excitations, which are produced by membrane operators. By considering a change of basis, we show that, in certain cases, some loop-like excitations represent domain walls between patches corresponding to different symmetry-related ground states, and we find this symmetry. We also map the higher lattice gauge theory Hamiltonian to the symmetry enriched string-net model for symmetry enriched topological phases (SETs) described by Heinrich, Burnell, Fidkowski and Levin [Phys. Rev. B, 94, 235136 (2016)], again in a subset of cases. |
| title | Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2204.05341 |