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Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension

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arxiv 2402.09520 v2 pith:VMAVY6BP submitted 2024-02-14 cond-mat.str-el hep-thquant-ph

Aswin Parayil Mana , Yabo Li , Hiroki Sukeno , Tzu-Chieh Wei This is my paper
classification cond-mat.str-elhep-thquant-ph
keywords symmetrytransformationkennedy-tasakimathbbphasessubsystemdualitykramers-wannier
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abstract

We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D transverse-field Ising model. Using the Kramers-Wannier duality operator, we also construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases, where the symmetry group for the former is either $\mathbb{Z}_2\times\mathbb{Z}_2$ or $\mathbb{Z}_2$. This generalizes the recently proposed picture of one-dimensional Kennedy-Tasaki transformation as a composition of manipulations involving gauging and stacking symmetry-protected topological phases to higher dimensions.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals

    cond-mat.str-el 2026-07 accept novelty 7.0 of 10

    In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.

  2. Symmetry theta angles and topological Witten effects

    hep-th 2025-06 conditional novelty 7.0 of 10

    Symmetry theta angles are intrinsic, Lagrangian-independent parameters of any non-anomalous Abelian invertible symmetry, and their universal effect is a topological Witten effect that shuffles twisted sectors while pr...

  3. Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Gravitational topological responses are shown to appear as the projective phase (ST)^3=Y in gauging/stacking relations, corresponding on the lattice to nontrivial QCAs implementable via finite-depth circuits, measurem...

  4. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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