Unnecessary quantum criticality in $SU (3)$ kagome magnets

No major weakness in my opinion.

The paper deals with the very relevant topic of Dirac spin liquids whose stability w.r.t. monopole proliferation is still unsettled.
The authors focus on the SU(3) Kagome antiferromagnet which has been largely unexplored and could be realized on cold atom platforms. The authors use advanced field theoretical tools to address the stability of the SU(3) DSL. They find that the SU(3) DSL is a so-called "unnecessary quantum critical point" that does not separate two distinct phases but instead lies within a single phase. They also argue this phase is the trimer phase of the NN SU(3) Heisenberg model on the Kagome lattice. I think this work meets all criteria to be published in Sci Post.

If the authors are correct that the DSL lies within the (two-fold degenerate) SU(3) trimer phase I would be curious to see whether it could be realized in the simple model studied in Ref. [55] simply upon tuning the ratio of the (real) 3-site permutation by the 2-site permutation (corresponding to the "equator" of the phase diagram of Fig. 1 showing an extended trimer phase) or whether a more complicated perturbation of the NN SU(3) Heisenberg model (large-U Hubbard model) has to be considered.

See above remark.

Publish (surpasses expectations and criteria for this Journal; among top 10%)

The paper presents an interesting new perspective on a class of U(1) Dirac spin liquid (DSL) states. Even if such states do not form stable phases due to the presence of a relevant, symmetry-allowed monopole operator, the authors argue that they can nevertheless be viewed as nontrivial quantum critical points when the monopole coupling is tuned to zero. The paper focuses on a particular scenario in which, regardless of the sign of the monopole term, the relevant perturbation always drives the DSL into the same stable phase. In this case, the DSL represents an “unnecessary quantum critical point,” a concept previously proposed by one of the authors.

I find the results interesting, and the paper is clearly written and well presented.

That said, as the authors themselves acknowledge in the abstract, the main conclusion remains conjectural. This is of course not a shortcoming specific to the present work, as the qualitative IR behavior of the DSL is generally a very difficult subject except in the large-Nf limit. The result of the paper relies on several aspects of the DSL that are not entirely established. For example, for the result of the paper to be correct, the double monopole needs to be irrelevant (discussions in page 5). The authors used the scaling dimension of the monopole operator evaluated in the large-Nf framework. While such large-Nf estimates appear empirically consistent even for small Nf in several known cases, it is unclear whether there are sufficient examples to establish the reliability of the large-Nf results in a definitive way, even at an empirical level.

According to the general guidelines for SciPost Physics, the paper may qualify under the second criterion: “opening a new pathway in an existing or new research direction, with clear potential for multi-pronged follow-up work.” This assessment depends on whether we view the subject of “unnecessary quantum critical point” as a research direction in its own right. If so, the present work does open a new pathway, as it suggests that this perspective can be applied to many previously studied spin liquid states.

I therefore leave the final decision to the editor.

Ask for minor revision

In the manuscript “Unnecessary Quantum Criticality in an SU(3) Kagome Magnet”, the authors focus on the Kagome-lattice Dirac spin liquid (DSL), described by (2+1)-dimensional quantum electrodynamics (QED3) with N_f = 6 Dirac fermions. They present a careful analysis of the UV symmetries, the emergent IR symmetries, and the quantum anomalies of this DSL. Based on this analysis, the authors argue that the DSL is an unnecessary quantum critical point that lies entirely within a single phase, plausibly the trimerized valence-bond-solid (VBS) phase. The analysis is technically sound, and the conclusion that the DSL represents an unnecessary critical point is both nontrivial and interesting. I believe this manuscript merits publication, provided that the authors properly address the following questions.

On page 2, the authors state that “To realize SU(3) symmetric interactions, one can use atoms with nuclear spin I=1/2 such as ^171Yb…”. However, the previous paragraph states that SU(N) models can be simulated for N \leq 2I +1, which contradicts the sentence above. Could the author clarify these statements?

Below Eq. (6), the inline equation “\oplus^3 3= 1 \otimes 8” seems to be a typo.

In the text, the notations for charge conjugation, time reversal, and spatial reflection are interchanged compared to Eqs. (16-18)

In Eq. (39), should it be \mathbb{Z}_6 instead of \mathbb{Z}^6?

Could the authors clarify how the UV time reversal acts? Naively, the time-reversal symmetry would exchange the fundamental and antifundamental representations of SU(3). If true, does the large-U-limit Mott insulator with one particle per site break the time-reversal symmetry? However, the text below Eq. (59) states that the VBS state (which is a Mott insulator) preserves the UV time-reversal symmetry.

In the scenario where the DSL is an unnecessary critical point within the VBS phase, the authors argued that the PSU(6)-symmetric DSL lives on a codimension-one surface in the parameter space. When the monopole condenses, the symmetry is broken to (SU(3) \times SU(3))/Z3. Does it mean that (SU(3) \times SU(3))/Z3 is an emergent symmetry in a “codimension-zero” regime of the parameter space within the VBS phase? If true, how should one understand the emergence of this large symmetry away from the critical point?

Ask for minor revision