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Generating Lattice Non-invertible Symmetries

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arxiv 2406.05454 v3 pith:AAUH66R7 submitted 2024-06-08 cond-mat.str-el hep-th

Weiguang Cao , Linhao Li , Masahito Yamazaki This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords non-invertiblesymmetrysymmetriesdipolelatticemathbbtransformationtransformations
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami $\mathbb Z_N\times\mathbb Z_N$ type, we obtain a new non-invertible symmetry in models with $\mathbb Z_N$ dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.

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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. Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

    cond-mat.str-el 2025-05 conditional novelty 7.0 of 10

    Exact many-body scar eigenstates of a 2D XY model are mapped via Kramers-Wannier duality to exact scars of a Z2 lattice gauge theory.

  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. Non-invertible translation from Lieb-Schultz-Mattis anomaly

    cond-mat.str-el 2026-01 conditional novelty 6.0 of 10

    Gauging the full internal symmetry of a lattice system with an LSM anomaly turns lattice translation into a non-invertible operator whose fusion rules involve condensation defects.

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