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Disordered nonFermi liquid fixed point for twodimensional metals at Isingnematic quantum critical points
by KyoungMin Kim, KiSeok Kim
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Submission summary
Authors (as registered SciPost users):  KyoungMin Kim 
Submission information  

Preprint Link:  scipost_202403_00028v1 (pdf) 
Date submitted:  20240320 09:37 
Submitted by:  Kim, KyoungMin 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of nonFermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of twodimensional nonFermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensionalregularized field theory for Isingnematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawatype interactions between electrons and bosonic orderparameter fluctuations in a perturbative epsilon expansion. At the oneloop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the twoloop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered nonFermi liquid (DNFL) fixed point.” Our investigation reveals that twoloop 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 pseudogaplike behavior in the electron's density of states. These findings shed light on the quantum critical behavior of disordered nonFermi liquid metals, emphasizing the indispensable role of higherorder loop corrections in such comprehension.
Current status:
Reports on this Submission
Report
The author has investigated the effect of disorder at the Isingnematic transition, claiming to have employed a controlled epsilon expansion to identify a new disordered fixed point at infinite N, up to the twoloop 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 higherloop corrections vanish in the large N limit?
4. Will higherloop 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?
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
1 The paper develops a new regulation technique to tackle disordered nonFermi liquid models within the codimension 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.
Weaknesses
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.
Report
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.
Recommendation
Ask for minor revision