SciPost Submission Page
Building 1D lattice models with $G$-graded fusion category
by Shang-Qiang Ning, Bin-Bin Mao, Chenjie Wang
Submission summary
| Authors (as registered SciPost users): | Chenjie Wang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202402_00006v1 (pdf) |
| Date submitted: | 2024-02-04 16:45 |
| Submitted by: | Wang, Chenjie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We construct a family of one-dimensional (1D) quantum lattice models based on $G$-graded unitary fusion category $\calC_G$. 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 $\calC_G$. 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.
Current status:
Reports on this Submission
Report
This paper gives a systematic construction of 1D lattice models using graded fusion category degrees of freedom. In particular, the authors take the graded fusion category data, define a constrained Hilbert space out of it, and determine the Hamiltonian that satisfies the graded fusion category symmetry. Several example Hamiltonians are then studied numerically and shown to contain gapless regions in the phase diagram. This is an interesting work, especially given the recent interest in categorical symmetries. Using the protocol given in this paper, one can systematically construct models with categorical symmetry that reflect the edge physics of 2D symmetry enriched phases. The paper is very carefully written and is a nice addition to the literature. I only have one minor comment: This paper https://arxiv.org/abs/2110.12882 seems to be on a related topic, although the result seems to be a subset of that in this paper. Can the authors comment on their relation?