Twisted Kitaev quantum double model as local topological order
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929731005317120 |
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| author | Cui, Shawn X. Galindo, César Romero, Diego |
| author_facet | Cui, Shawn X. Galindo, César Romero, Diego |
| contents | We study the Twisted Kitaev Quantum Double model within the framework of Local Topological Order (LTO). We extend its definition to arbitrary 2D lattices, enabling an explicit characterization of the ground state space through the invariant spaces of monomial representations. We reformulate the LTO conditions to include general lattices and prove that the twisted model satisfies all four LTO axioms on any 2D lattice. As a corollary, we show that its ground state space is a quantum error-correcting code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Kitaev quantum double model as local topological order Cui, Shawn X. Galindo, César Romero, Diego Quantum Algebra We study the Twisted Kitaev Quantum Double model within the framework of Local Topological Order (LTO). We extend its definition to arbitrary 2D lattices, enabling an explicit characterization of the ground state space through the invariant spaces of monomial representations. We reformulate the LTO conditions to include general lattices and prove that the twisted model satisfies all four LTO axioms on any 2D lattice. As a corollary, we show that its ground state space is a quantum error-correcting code. |
| title | Twisted Kitaev quantum double model as local topological order |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2411.08675 |