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Building 1D lattice models with $G$-graded fusion category
by Shang-Qiang Ning, Bin-Bin Mao, Chenjie Wang
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Chenjie Wang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202402_00006v2 (pdf) |
| Date accepted: | 2024-10-16 |
| Date submitted: | 2024-09-06 17:37 |
| Submitted by: | Wang, Chenjie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct a family of one-dimensional (1D) quantum lattice models based on $G$-graded unitary fusion category $\mathcal{C}_G$. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category $\mathcal{C}_G$. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.
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- 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
We thank the referees for very positive reports. Both of them consider our work of high validity and originality. Referee 1 only asks a minor question about the relation of our work to another work in the literature. While Referee 2 asks many questions, they are all about conceptual or technical clarifications, or about presentation issues of the manuscript. We have replied to all the questions below, and have revised the manuscript according to the suggestions of the referees. We hope the revised manuscript is ready for publication in SciPost.
Yours Sincerely,
Shangqiang Ning, Bin-Bin Mao and Chenjie Wang
List of changes
1. Added the phase diagram of $H^0$ in Fig. 3.
2. Revised a few paragraphs of Section 3.2.1 due to the addition of the phase diagram of $H^0$.
3. Minor revisions of the presentation in several places suggested by Referees
Published as SciPost Phys. 17, 125 (2024)