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Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
by Bram Vancraeynest-De Cuiper, Clement Delcamp
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Clement Delcamp · Bram Vancraeynest-De Cuiper |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2501.16301v1 (pdf) |
| Date submitted: | March 3, 2025, 5:01 p.m. |
| Submitted by: | Bram Vancraeynest-De Cuiper |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2025-5-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2501.16301v1, delivered 2025-05-24, doi: 10.21468/SciPost.Report.11259
Report
I recommend the draft for publication, pending the following minor revision:
While the paper is technically precise, it is difficult to follow, particularly for readers not already familiar with the authors’ notation. I suggest including a summary or roadmap for Sections 2 and 3. For example, it would be helpful to clearly outline the starting point (e.g., the Hamiltonian and its global symmetry), the gauging operations or duality transformations applied, and the resulting theory (with its new Hamiltonian and symmetry). This overview could be presented in a concise table or descriptive paragraph, either in the introduction or at the end of each relevant subsection.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #2 by Anonymous (Referee 2) on 2025-5-22 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2501.16301v1, delivered 2025-05-22, doi: 10.21468/SciPost.Report.11245
Report
In this paper, the authors develop a systematic formulation of duality on quantum lattice models with an invertible symmetry. In 1+1 dimension, the original lattice model is assumed to have a conventional Abelian invertible (0-form) symmetry. Then the duality is defined by an untwisted gauging of the symmetry followed by a twisted gauging of the dual symmetry, which also has a tensor-network representation. For the $\mathbb{Z}_p \times \mathbb{Z}_p$ symmetry, the duality thus defined reproduces the well known Kennedy-Tasaki transformation. The authors then extend the formulation to lattice gauge theories in 2+1 dimensions, to formulate the duality as a untwisted gauging of the 1-form symmetry (of the original lattice gauge model) followed by a twisted gauging of the dual 0-form symmetry. As in 1+1 dimensions, there is a nontrivial interplay between the symmetry-twisted boundary conditions and charge sectors under the duality. This paper gives a general perspective for the Kennedy-Tasaki duality in 1+1 dimension and further provides interesting novel results on duality on lattice gauge theories in 2+1 dimensions. I recommend publication of this paper in SciPost Physics. However I would like to ask the authors to consider the following points.
1) The notation $\mathfrak{x}_v$ is confusing as it actually depends on $x$ but it is not easy to relate $x$ with $\mathfrak{x}$. Maybe you can introduce another symbol and put $x$ in superscript (if this does not cause other problems). 2) (this is optional) Do you have any insight/comment on systems on 1d lattice other than simple chains (such as 2-leg ladders)? Essentially they are 1+1 dimensional but in some sense they are between 1+1 and 2+1 dimensions ($n$-leg ladder in $n \to \infty$ limit is the 2d square lattice).
Recommendation
Ask for minor revision