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Lattice Models for Phases and Transitions with Non-Invertible Symmetries
by Lakshya Bhardwaj, Lea E. Bottini, Sakura Schafer-Nameki, Apoorv Tiwari
Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj · Apoorv Tiwari |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.05964v3 (pdf) |
| Date submitted: | 2024-08-27 16:09 |
| Submitted by: | Tiwari, Apoorv |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Non-invertible categorical symmetries have emerged as a powerful tool to uncover new beyond-Landau phases of matter, both gapped and gapless, along with second order phase transitions between them. The general theory of such phases in (1+1)d has been studied using the Symmetry Topological Field Theory (SymTFT), also known as topological holography. This has unearthed the infrared (IR) structure of these phases and transitions. In this paper, we describe how the SymTFT information can be converted into an ultraviolet (UV) anyonic chain lattice model realizing, in the IR limit, these phases and transitions. In many cases, the Hilbert space of the anyonic chain is tensor product decomposable and the model can be realized as a quantum spin-chain Hamiltonian. We also describe operators acting on the lattice models that are charged under non-invertible symmetries and act as order parameters for the phases and transitions. In order to fully describe the action of non-invertible symmetries, it is crucial to understand the symmetry twisted sectors of the lattice models, which we describe in detail. Throughout the paper, we illustrate the general concepts using the symmetry category $\mathsf{Rep}(S_3)$ formed by representations of the permutation group $S_3$, but our procedure can be applied to any fusion category symmetry.
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
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In this paper, the authors study lattice models with various non-invertible symmetries and study their phase diagrams. The subject is at the forefront of the current research in theoretical physics, and the obtained results are quite interesting. I recommend publication of this paper.
I just have one request: can the authors summarize/showcase the lattice models (and maybe phase diagram -- although it would be also fine to give pointers to the relevant sections) they constructed, in a single place (either in Introduction, Summary, or even Appendix)? It requires a lot of effort and time to go through the paper especially for non-experts on the subject. However, even non-experts could check the lattice models and play with them numerically if presented accessibly.
Recommendation
Ask for minor revision