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Subsystem Non-Invertible Symmetry Operators and Defects

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arxiv 2304.09886 v3 pith:WTIAXERK submitted 2023-04-19 cond-mat.str-el hep-th

Weiguang Cao , Linhao Li , Masahito Yamazaki , Yunqin Zheng This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords subsystemdefectsdualitykramers-wannieroperatorssymmetryfusiongauging
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abstract

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

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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. Lattice non-invertible symmetry from non-commuting transfer matrices

    cond-mat.stat-mech 2026-06 unverdicted novelty 8.0 of 10

    For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.

  2. 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.

  3. 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.

  4. 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...

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