Quantum Cluster State Model with Haagerup Fusion Category Symmetry
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909877007286272 |
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| author | Jia, Zhian |
| author_facet | Jia, Zhian |
| contents | We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra $H_3$ from the Haagerup fusion category, ensuring that the representation category of $H_3$ is equivalent to Haagerup fusion category. Utilizing the framework of symmetry topological field theory (SymTFT), we develop an ultra-thin weak Hopf quantum double model, characterized by a smooth topological boundary condition. We show that this model supports Haagerup fusion category symmetry. Finally, we solve the ground state of the model in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion category symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19657 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Cluster State Model with Haagerup Fusion Category Symmetry Jia, Zhian Quantum Algebra Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra $H_3$ from the Haagerup fusion category, ensuring that the representation category of $H_3$ is equivalent to Haagerup fusion category. Utilizing the framework of symmetry topological field theory (SymTFT), we develop an ultra-thin weak Hopf quantum double model, characterized by a smooth topological boundary condition. We show that this model supports Haagerup fusion category symmetry. Finally, we solve the ground state of the model in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion category symmetry. |
| title | Quantum Cluster State Model with Haagerup Fusion Category Symmetry |
| topic | Quantum Algebra Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.19657 |