Tensor networks for non-invertible symmetries in 3+1d and beyond
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912671164530688 |
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| author | Gorantla, Pranay Shao, Shu-Heng Tantivasadakarn, Nathanan |
| author_facet | Gorantla, Pranay Shao, Shu-Heng Tantivasadakarn, Nathanan |
| contents | Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing the Wegner duality in 3+1d lattice $\mathbb{Z}_2$ gauge theory. The non-invertible algebra, which mixes with lattice translations, can be efficiently computed using ZX-calculus. We further deform the $\mathbb{Z}_2$ gauge theory while preserving the duality and find a model with nine exactly degenerate ground states on a torus, consistent with the Lieb-Schultz-Mattis-type constraint imposed by the symmetry. Finally, we provide a ZX-diagram presentation of the non-invertible duality operators (including non-invertible parity/reflection symmetries) of generalized Ising models based on graphs, encompassing the 1+1d Ising model, the three-spin Ising model, the Ashkin-Teller model, and the 2+1d plaquette Ising model. The mixing (or lack thereof) with spatial symmetries is understood from a unifying perspective based on graph theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor networks for non-invertible symmetries in 3+1d and beyond Gorantla, Pranay Shao, Shu-Heng Tantivasadakarn, Nathanan Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing the Wegner duality in 3+1d lattice $\mathbb{Z}_2$ gauge theory. The non-invertible algebra, which mixes with lattice translations, can be efficiently computed using ZX-calculus. We further deform the $\mathbb{Z}_2$ gauge theory while preserving the duality and find a model with nine exactly degenerate ground states on a torus, consistent with the Lieb-Schultz-Mattis-type constraint imposed by the symmetry. Finally, we provide a ZX-diagram presentation of the non-invertible duality operators (including non-invertible parity/reflection symmetries) of generalized Ising models based on graphs, encompassing the 1+1d Ising model, the three-spin Ising model, the Ashkin-Teller model, and the 2+1d plaquette Ising model. The mixing (or lack thereof) with spatial symmetries is understood from a unifying perspective based on graph theory. |
| title | Tensor networks for non-invertible symmetries in 3+1d and beyond |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.12978 |