Tensor networks for non-invertible symmetries in 3+1d and beyond
| Autor: | Gorantla, Pranay, Shao, Shu-Heng, Tantivasadakarn, Nathanan |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 72+1 pages, 11 (numbered) figures, 2 tables |
| Databáze: | arXiv |
| Externí odkaz: |
|