Skeleton of Isometric Tensor Network States for Abelian String-Net Models.

Authors

Julian Boesl, Yu-Jie Liu, Frank Pollmann, Michael Knap

Published in

Physical review letters. Volume 137. Issue 2. Pages 020405. Jul 10, 2026.

Abstract

We construct parametrized isometric tensor network states-referred to as "skeletons"-that allow us to explore phases of Abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for Abelian topological order but also provide a nontrivial test bed for quantum processors.

PMID:
42503093
Bibliographic data and abstract were imported from PubMed on 26 Jul 2026.

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