SciPost Submission Page
Chiral Edge States Emerging on Anyon-Net
by Atsushi Ueda, Kansei Inamura, Kantaro Ohmori
Submission summary
| Authors (as registered SciPost users): | Kantaro Ohmori · Atsushi Ueda |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2408.02724v2 (pdf) |
| Date submitted: | 2024-08-26 10:49 |
| Submitted by: | Ueda, Atsushi |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We propose a symmetry-based approach to constructing lattice models for chiral topological phases, focusing on non-Abelian anyons. Using a 2+1D version of anyon chains and modular tensor categories(MTCs), we ensure exact MTC symmetry at the microscopic level. Numerical simulations using tensor networks demonstrate chiral edge modes for topological phases with Ising and Fibonacci anyons. Our method contrasts with conventional solvability approaches, providing a new theoretical avenue to explore strongly coupled 2+1D systems, revealing chiral edge states in non-Abelian anyonic systems.
Author indications on fulfilling journal expectations
- Address an important (set of) problem(s) in the field using appropriate methods with an above-the-norm degree of originality
- Detail one or more new research results significantly advancing current knowledge and understanding of the field.
Current status:
Reports on this Submission
Strengths
1- new construction of lattice model that stabilizes non-abelian chiral topological order
2- strong numerics with state-of-the-art tensor network methods
3- convincing signatures of topological order
Weaknesses
1- determination of the phase diagram is not established
Report
In this work, the authors introduce lattice models that realize phases with non-abelian chiral topological order. The idea for the construction, which is (2+1)D generalization of anyon chains, was introduced in an earlier work by some of the authors, but there the occurence of chiral topological phases was only hinted at. In this work, therefore, the authors consider a model with an explicitly chiral term, and use numerical simulations to show that the model exhibits chiral topological order for parts of the phase diagram.
The exploration of lattice models with (non-abelian) chiral topological order is an active research direction, in the context of spin liquids and fractional Chern insulators. In that respect, this work opens up a new, important, avenue for further explorations. In particular, the MTC symmetry is introduced explicitly at the microscopic level, which makes the construction very transparent and interesting.
The numerical simulations make use of tensor network parametrizations that explicitly encode the anyonic symmetry of the microscopic model, which is definitely the state-of-the-art method for simulating these types of models. The simulations are convincing that there is a part of the phase diagram that stabilizes a chiral topological order, as showcased beautifully by the extraction of the central charge and the entanglement spectrum on the open strip geometry.
For these reasons, I recommend publication of this manuscript.
I have one concern with the author's claim that there is a region in the phase diagram where the topological phase is stabilized, based on the results in Fig. 3. At the smallest values of H (in panels a and c), the divergence of the correlation length seems to be at a single point. In the inset of panels b and d, there is evidence that the central charge scaling is observed for more points in the vicinity as well. I don't think this is clear evidence for an extended phase: an equally plausible explanation is that these different points are all in the scaling region of this single critical point. Based on the numerical evidence, therefore, I don't believe the authors can make any definite claim about the topological phase boundaries.
I was wondering why the authors did not consider the use of cylindrical boundary conditions instead of the strip geometry. In that set-up, the phase boundaries and phase transitions should be more clearly visible and there's other signatures of topological order such as k-resolved entanglement spectra and topological entanglement entropy. This is rather standard practice in the numerical study of chiral spin liquids and fractional Chern insulators.
Requested changes
1- Reconsider claims on the phase diagrams for both models
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)