Comment on "Emergence of Nodal-Knot Transitions by Disorder"

TL;DR

This paper critiques a recent study on disorder-induced nodal-knot transitions, highlighting fundamental flaws in the RG analysis and phase transition criteria that undermine its conclusions.

Contribution

It provides a critical analysis pointing out errors in the previous work's methodology and invalidates its claims about disorder-driven nodal-knot transitions.

Findings

Identifies incorrect momentum space analysis in the criticized paper.

Shows the phase transition criterion used is invalid.

Demonstrates that claimed transitions can occur in clean systems.

Abstract

In a recent paper arXiv:2409.01034, Gong et al. studied the disorder effects in nodal-knot semimetal through Wilson momentum-shell renormalization group (RG) method. They stated that various nodal-knot transitions emerge driven by disorders. However, we notice that there are serious problems in this paper. First, in this paper, the RG analysis is not performed in the momentum space around the Fermi surface but in an incorrect momentum space around the point $k=0$. Accordingly, the RG equations are completely unreliable. Second, the criterion for phase transition employed in this paper is invalid. Accroding to the criterion in this paper, we can find that the various phase transitions stated in this paper even emerge in clean nodal-knot semimetal system! Thus, the conclusions in this paper are unfounded.