From gauging to duality in one-dimensional quantum lattice models

Bram Vancraeynest-De Cuiper; José Garre Rubio; Frank Verstraete; Kevin Vervoort; Dominic J. Williamson; Laurens Lootens

doi:10.21468/SciPostPhys.20.4.113

From gauging to duality in one-dimensional quantum lattice models

Bram Vancraeynest-De Cuiper (Corresponding author)
, José Garre Rubio
, Frank Verstraete
, Kevin Vervoort
, Dominic J. Williamson
, Laurens Lootens

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making use of matrix product operators, which provide the lattice representation theory for global (categorical) symmetries as well as a classification of duality transformations. Our construction makes the symmetries of the gauged theory manifest and clarifies how to deal with static background fields when gauging generalised symmetries.

Original language	English
Article number	113
Pages (from-to)	1-35
Journal	SciPost Physics
Volume	20
DOIs	https://doi.org/10.21468/SciPostPhys.20.4.113
Publication status	Published - 15 Apr 2026

Funding

Fudning information This work has received funding from the Research Foundation Flanders (FWO) through Ph.D. fellowship No. 11O2423N awarded to BVDC, EOS (Grant No. 40007526), IBOF (Grant No. IBOF23/064), and BOF-GOA (Grant No. BOF23/GOA/021). It is also funded via UKRI grant EP/Z003342/1, and ERC-CoG SEQUAM (Grant Agreement No. 863476). JGR is funded by the FWF Erwin Schrödinger Program (Grant DOI 10.55776/J4796). DJW is supported by the Australian Research Council Discovery Early Career Research Award (DE220100625). L.L. is supported by an EPSRC Postdoctoral Fellowship (grant No. EP/Y020456/1).

Austrian Fields of Science 2012

101028 Mathematical modelling
103036 Theoretical physics
103025 Quantum mechanics

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10.21468/SciPostPhys.20.4.113Licence: CC BY 4.0

Cite this

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From gauging to duality in one-dimensional quantum lattice models

Abstract

Funding

Austrian Fields of Science 2012

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Generalized symmetries in quantum tensor networks

SEQUAM: Symmetries and Entanglement in Quantum Matter

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From gauging to duality in one-dimensional quantum lattice models

Abstract

Funding

Austrian Fields of Science 2012

Access to Document

Other files and links

Projects

Generalized symmetries in quantum tensor networks

SEQUAM: Symmetries and Entanglement in Quantum Matter

Cite this