SciPost Submission Page
Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
by Bram Vancraeynest-De Cuiper, Clement Delcamp
Submission summary
| Authors (as registered SciPost users): | Clement Delcamp · Bram Vancraeynest-De Cuiper |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00050v1 (pdf) |
| Date accepted: | July 29, 2025 |
| Date submitted: | July 18, 2025, 10:13 a.m. |
| Submitted by: | Bram Vancraeynest-De Cuiper |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| 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
Author comments upon resubmission
Referee 3:
\emph{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.}
Following the referee’s suggestion, we added a table in the introduction that summarises the main results of our manuscript.
Referee 2:
\emph{1) The notation $\mathfrak x_{\mathsf v}$ 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). }
We agree with the referee that this notation, and especially its dependence on $x$, was confusing. In the revised version of the manuscript, although we maintained the use of $\mathfrak x_{\mathsf v}$, we clarified its meaning and are no longer referring to another $x$. Concretely, a function $\mathfrak x_{\mathsf v} : \mathsf V \to G$ is such that it only assigns a non-trivial element to $\mathsf v$. By summing over $\mathfrak x_{\mathsf v}$, we are summing over all possible values in $G$ this function can assign to $\mathsf v$.
\emph{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).}
It is our understanding that a 2-leg ladder, and generalisations thereof, can be rewritten as a spin chain with a larger local Hilbert space and/or longer range interactions. Our method accommodates both generalisations with no modifications.
Published as SciPost Phys. 19, 054 (2025)