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2D Fractons from Gauging Exponential Symmetries
by Guilherme Delfino, Claudio Chamon, Yizhi You
Submission summary
| Authors (as registered SciPost users): | Guilherme Delfino |
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| Preprint Link: | https://arxiv.org/abs/2306.17121v3 (pdf) |
| Date submitted: | 2023-08-11 14:59 |
| Submitted by: | Delfino, Guilherme |
| Submitted to: | SciPost Physics |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
The scope of quantum field theory is extended by introducing a broader class of discrete gauge theories with fracton behavior in 2+1D. We consider translation invariant systems that carry special charge conservation laws, which we refer to as exponential polynomial symmetries. Upon gauging these symmetries, the resulting $\mathbb{Z}_N$ gauge theories exhibit fractonic physics, including constrained mobility of quasiparticles and UV dependence of the ground state degeneracy. For appropriate values of theory parameters, we find a family of models whose excitations, albeit being deconfined, can only move in the form of bound states rather than isolated monopoles. For concreteness, we study in detail the low-energy physics and topological sectors of a particular model through a universal protocol, developed for determining the holonomies of a given theory. We find that a single excitation, isolated in a region of characteristic size $R$, can only move from its original position through the action of operators with support on $\mathcal{O}(R)$ sites. Furthermore, we propose a Chern-Simons variant of these gauge theories, yielding non-CSS type stabilizer codes, and propose the exploration of exponentially symmetric subsystem SPTs and fracton codes in 3+1D.
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Report
In this work, the authors make an argument that there are the 2D fracton topological orders in the two-dimensions. However, the previous work for a long time in the community has shown from various ways that fracton topological orders can only exist in 3D and higher. This obvious conflict must be addressed explicitly and clearly in the main text. The authors should explain why their conclusions are different from D. Aasen, D. Bulmash, A. Prem, K. Slagle and D. J. Williamson, Phys. Rev. Research 2, 043165 (2020) and J. Haah, arXiv:1812.11193. The former paper is cited as Ref. [43] in this manuscript and only appears once (page 3) and latter paper is not cited. There are detailed discussions on the issues in Section V in Ref. [43]. I think the authors must explain why their models can avoid the no-go result given by Ref. 43 and also compare their results with Haah's analysis. Unfortunately, I did not see such discussions in the present manuscript. In fact, the quantity R can be very large but always finite, which means that the excitations can be moved at the end of day. We must agree that, defining a phase must be in the thermodynamical limit.
In addition, a technical concern is that, in general, we should perform symmetry transformation explicitly on the field (boson/electron creation/annihliation) operators to demonstrate how operators are transformed under the symmetry operation. After this is clearly done, one can safely do the gauging by Peierls substitution. In Section 2.1, I did not see such standard procedure but a direct shift into gauging shown in eqs. 2.4. I think it is important to perform the above standard procedure carefully as gauging a group must be done after the symmetry operation is clearly defined.