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Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

by Kyoung-Min Kim, Ki-Seok Kim

This is not the latest submitted version.

Submission summary

Authors (as registered SciPost users): Kyoung-Min Kim
Submission information
Preprint Link: scipost_202403_00028v1  (pdf)
Date submitted: 2024-03-20 09:37
Submitted by: Kim, Kyoung-Min
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point.” Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron's density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2024-4-26 (Invited Report)


The author has investigated the effect of disorder at the Ising-nematic transition, claiming to have employed a controlled epsilon expansion to identify a new disordered fixed point at infinite N, up to the two-loop order. They further argue that this fixed point persists at finite N and with higher order corrections. This is a solid piece of work and is definitely publishable. However, I am still trying to understand more about this research. I will recommend its publication once my following questions are fully addressed:
1. Is the calculation controlled around epsilon=0 and N=infty? This would imply that a double expansion in epsilon and 1/N is necessary. Was this paper actually employed this double expansion?
2. If the answer is yes, as the disordered fixed point manifest only at finite epsilon, does this suggest that the direct study of such a fixed point is not controlled?
3. Do all higher-loop corrections vanish in the large N limit?
4. Will higher-loop corrections alter the location of the disordered fixed point? Considering that the presence or position of the fixed point is determined by the beta function's solutions, how can we ensure that these solutions consistently exist?


Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: high
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2024-4-24 (Invited Report)


1- The paper develops a new regulation technique to tackle disordered non-Fermi liquid models within the co-dimension expansion which avoids UV/IR mixing up to 2 loops.

2- The authors discover a new disordered fixed point at 2 loop order which doesn't exist at 1 loop.


1- The authors use a small codimension as well as large $N$ expansion to control the perturbative expansion. However the disordered fixed point that they discover at 2 loops only exists beyond a critical value of the codimension ($\epsilon > \epsilon_c \approx 0.41$) in the limit $N\rightarrow\infty$. This brings into question the robustness of the existence of this disordered fixed point to higher loop corrections. The question of whether this disordered fixed point survives higher loop corrections is left open.


The submission meets the criteria for publication in SciPost with a few minor revisions to clarify the effect of higher loops corrections on the disordered fixed point.

Requested changes

1- Addition of a discussion on the fate of the disordered fixed point to higher loop corrections, specifically how robust the critical value $\epsilon_c$ is to such corrections. A few comments on whether this critical value is prevented from being larger than the physical value $\epsilon = 0.5$ are warranted.


Ask for minor revision

  • validity: good
  • significance: good
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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