Tensor networks for non-invertible symmetries in 3+1d and beyond

• URL: http://arxiv.org/abs/2406.12978v1
• Date: Tue, 18 Jun 2024 18:00:15 GMT
• Title: Tensor networks for non-invertible symmetries in 3+1d and beyond
• Authors: Pranay Gorantla, Shu-Heng Shao, Nathanan Tantivasadakarn,
• Abstract summary: We use ZX-diagrams to define a non-invertible operator implementing the Wegner duality in 3+1d lattice $mathbbZ$ gauge theory. We further deform the $mathbbZ$ gauge theory while preserving the duality and find a model with nine exactly ground states on a torus.
• Score: 0.13654846342364307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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