Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories
Given a two-dimensional quantum lattice model with an Abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a twisted way via a choice of discrete torsion. Using tensor netw...
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2025-08-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.2.054 |
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| author | Bram Vancraeynest-De Cuiper, Clement Delcamp |
| author_facet | Bram Vancraeynest-De Cuiper, Clement Delcamp |
| author_sort | Bram Vancraeynest-De Cuiper, Clement Delcamp |
| collection | DOAJ |
| description | Given a two-dimensional quantum lattice model with an Abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a twisted way via a choice of discrete torsion. Using tensor networks, we introduce explicit lattice realisations of the so-called condensation defects, which are obtained by gauging the 1-form symmetry along submanifolds of spacetime, and employ the same calculus to realise the duality operators. By leveraging these tensor network operators, we compute the non-trivial interplay between symmetry-twisted boundary conditions and charge sectors under the duality operation, enabling us to construct isometries relating the dual Hamiltonians. Whenever a lattice gauge theory is left invariant under the duality operation, we explore the possibility of promoting the self-duality to an internal symmetry. We argue that this results in a symmetry structure that encodes the 2-representations of a 2-group. |
| format | Article |
| id | doaj-art-80cbb76e00f64b51807a40d65551ccc0 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-80cbb76e00f64b51807a40d65551ccc02025-08-22T13:43:14ZengSciPostSciPost Physics2542-46532025-08-0119205410.21468/SciPostPhys.19.2.054Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theoriesBram Vancraeynest-De Cuiper, Clement DelcampGiven a two-dimensional quantum lattice model with an Abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a twisted way via a choice of discrete torsion. Using tensor networks, we introduce explicit lattice realisations of the so-called condensation defects, which are obtained by gauging the 1-form symmetry along submanifolds of spacetime, and employ the same calculus to realise the duality operators. By leveraging these tensor network operators, we compute the non-trivial interplay between symmetry-twisted boundary conditions and charge sectors under the duality operation, enabling us to construct isometries relating the dual Hamiltonians. Whenever a lattice gauge theory is left invariant under the duality operation, we explore the possibility of promoting the self-duality to an internal symmetry. We argue that this results in a symmetry structure that encodes the 2-representations of a 2-group.https://scipost.org/SciPostPhys.19.2.054 |
| spellingShingle | Bram Vancraeynest-De Cuiper, Clement Delcamp Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories SciPost Physics |
| title | Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories |
| title_full | Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories |
| title_fullStr | Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories |
| title_full_unstemmed | Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories |
| title_short | Twisted gauging and topological sectors in (2+1)d Abelian lattice gauge theories |
| title_sort | twisted gauging and topological sectors in 2 1 d abelian lattice gauge theories |
| url | https://scipost.org/SciPostPhys.19.2.054 |
| work_keys_str_mv | AT bramvancraeynestdecuiperclementdelcamp twistedgaugingandtopologicalsectorsin21dabelianlatticegaugetheories |