Tensor Networks for Noninvertible Symmetries in 3+1D and Beyond
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p32z-v884.pdf
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4.48 MB
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Author(s)
Gorantla, Pranay
Shao, Shu-Heng
Tantivasadakarn, Nathanan
Date Issued
October 8, 2025
Journal
Physical Review X
Publisher
American Physical Society (APS)
Citation
Gorantla, Pranay, Shao, Shu-Heng and Tantivasadakarn, Nathanan. 2025. "Tensor Networks for Noninvertible Symmetries in 3+1D and Beyond." Physical Review X, 15 (4).
Version
Final published version
Abstract
Tensor networks provide a natural language for noninvertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a noninvertible operator implementing the Wegner duality in 3+1D lattice ℤ2 gauge theory. The noninvertible algebra, which mixes with lattice translations, can be efficiently computed using ZX-calculus. We further deform the ℤ2 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 noninvertible duality operators (including noninvertible parity and 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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1103/p32z-v884
