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Generalized Kramers-Wannier Duality from Bilinear Phase Map

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arxiv 2403.16017 v3 pith:36YEOXUF submitted 2024-03-24 cond-mat.str-el cond-mat.stat-mechmath-phmath.MP

Linhao Li , Masaki Oshikawa , Han Yan This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mechmath-phmath.MP
keywords dualityanomalybilinearclassdualitiesgeneralgeneralizedkramers-wannier
verification ladder T0 review T1 audit T2 compute T3 formal
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We present the bilinear phase map (BPM), a concept that generalizes the Kramers-Wannier (KW) transformation to investigate unconventional gapped phases of qudit spin chains. Encoding the transformation in a matrix, the BPM enables the exploration of a broader spectrum of generalized quantum phases and dualities, including the nonunitarity in duality transformations, and derivation of general noninvertible fusion rules. Furthermore, we obtain strong constraints on anomaly conditions of qudit models with a general class of duality symmetries. This establishes a microscopic anomaly classification for a broad class of lattice dualities.

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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. Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond

    cond-mat.str-el 2026-03 accept novelty 6.0 of 10

    A generalized MPS push-through condition for modulated symmetries classifies 1D SPTs and yields LSM constraints via site-dependent virtual cocycles.

  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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