SciPost Submission Page
Linear Resistivity from Spatially Random Interactions and the Uniqueness of Yukawa Coupling
by Sang-Jin Sin, Yi-Li Wang
Submission summary
| Authors (as registered SciPost users): | Yili Wang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202511_00033v1 (pdf) |
| Date submitted: | Nov. 17, 2025, 9:57 a.m. |
| Submitted by: | Yili Wang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form $(\psi^{\dagger}\psi)^n\phi^m$ in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only spatially random Yukawa-type interaction in $(2+1)$ dimensions can yield linear resistivity.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Awaiting resubmission
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2026-1-23 (Invited Report)
Disclosure of Generative AI use
The referee discloses that the following generative AI tools have been used in the preparation of this report:
I used AI to check the grammar in my report
Report
This is an interesting paper that considers models with general interactions of the form $(\psi^\dagger\psi)^n\phi^m$ with random couplings, and analyzes them in a large-$N$ Schwinger–Dyson framework. The main result is the claim that within this family, linear-in-$T$ resistivity appears only for the spatially random Yukawa coupling with $n=m=1$ in $d=2$. I think the question is well motivated.
The analytical solution of the large-$N$ Schwinger–Dyson equations is carried out through a sequence of assumptions, approximations, and complicated Feynman integrals. Many of these derivations rely on, or closely follow, similar steps in previous papers [8], [11], [16], [20].
The main new general integral is given in Eqs. (2.30) and (2.36). The authors claim that it scales as in Eq. (2.37). In my opinion, this is the most important technical result of the paper, yet it is not derived or explained rigorously enough.
For example, the special case $m=n=1$ of the self-energy is computed for arbitrary $d$ in Eq. (2.34), but that result is not fully correct: at $d=2$ there is an additional $\log(\Omega)$ factor, as derived in Ref. [8]. Moreover, for $d \geq 2$ the integral is divergent and must be regularized; the leading divergence comes with $\Omega$ factor. The authors do not explain how this integral should be regularized and how the divergence is handled. The integral in Eq. (2.31) is divergent as well, and the result in Eq. (2.32) must contain a divergent term, only $\Pi(\Omega)-\Pi(0)$ is divergence-free in this case. The authors do not mention this either.
These are just particular examples for $m=n=1$, but the same divergence issues will unavoidably arise in the general integral in Eq. (2.30). Therefore, the derivation of Eq. (2.37) should be treated with extreme care and supplemented with a detailed explanation. The authors should explain how this integral is regularized, what the divergences are, and how these divergences affect the final conclusion—or, alternatively, why they do not affect it. I also find that several derivations in the appendices are not well explained and again avoid discussing the divergent parts.
If the authors include all these additional details, I would recommend the article for publication in SciPost.
The analytical solution of the large-$N$ Schwinger–Dyson equations is carried out through a sequence of assumptions, approximations, and complicated Feynman integrals. Many of these derivations rely on, or closely follow, similar steps in previous papers [8], [11], [16], [20].
The main new general integral is given in Eqs. (2.30) and (2.36). The authors claim that it scales as in Eq. (2.37). In my opinion, this is the most important technical result of the paper, yet it is not derived or explained rigorously enough.
For example, the special case $m=n=1$ of the self-energy is computed for arbitrary $d$ in Eq. (2.34), but that result is not fully correct: at $d=2$ there is an additional $\log(\Omega)$ factor, as derived in Ref. [8]. Moreover, for $d \geq 2$ the integral is divergent and must be regularized; the leading divergence comes with $\Omega$ factor. The authors do not explain how this integral should be regularized and how the divergence is handled. The integral in Eq. (2.31) is divergent as well, and the result in Eq. (2.32) must contain a divergent term, only $\Pi(\Omega)-\Pi(0)$ is divergence-free in this case. The authors do not mention this either.
These are just particular examples for $m=n=1$, but the same divergence issues will unavoidably arise in the general integral in Eq. (2.30). Therefore, the derivation of Eq. (2.37) should be treated with extreme care and supplemented with a detailed explanation. The authors should explain how this integral is regularized, what the divergences are, and how these divergences affect the final conclusion—or, alternatively, why they do not affect it. I also find that several derivations in the appendices are not well explained and again avoid discussing the divergent parts.
If the authors include all these additional details, I would recommend the article for publication in SciPost.
Recommendation
Ask for major revision
Strengths
Models similar to the one studied here have been intensely discussed recently. Hence, the overall topic is certainly timely. The presentation of the analysis is very clear and the results appear correct.
Weaknesses
As discussed in more detail in the report, the findings of this manuscript are rather obvious and unsurprising.
Report
The manuscript studies a class of spatially random, SYK-inspired interactions between fermions and critical scalar bosons of the form $ (\psi^\dagger \psi)^n \phi^m $ in arbitrary spatial dimensions. Using the large-$N$ saddle-point ($G-\Sigma$) formalism, the authors classify the scaling behavior of and bosonic self-energies and compute the resulting conductivity via the Kubo formula, employing the fact that vertex corrections vanish for a local fermion self-energy. By combining dimensional analysis with explicit evaluations, they conclude that linear-in-temperature resistivity arises uniquely from a spatially random Yukawa coupling $m=n=1$ for two spatial dimensions, while all other couplings or higher dimensions lead to different power-law behavior (with larger resistivity exponents).
While the analysis is technically competent, the overall approach is rather straightforward. The main results follow almost entirely from power counting and scaling arguments once the structure of the interaction is specified. The explicit calculations largely confirm what is already evident from dimensional analysis, and the conclusion - that only the previously studied 2D random Yukawa coupling yields linear resistivity - is not surprising. The work does not uncover new physical mechanisms, qualitatively new phenomena, or unexpected results beyond a systematic but routine classification exercise. As such, the manuscript does not meet the novelty or conceptual depth expected for publication in this journal, and I therefore do not recommend it for publication.
While the analysis is technically competent, the overall approach is rather straightforward. The main results follow almost entirely from power counting and scaling arguments once the structure of the interaction is specified. The explicit calculations largely confirm what is already evident from dimensional analysis, and the conclusion - that only the previously studied 2D random Yukawa coupling yields linear resistivity - is not surprising. The work does not uncover new physical mechanisms, qualitatively new phenomena, or unexpected results beyond a systematic but routine classification exercise. As such, the manuscript does not meet the novelty or conceptual depth expected for publication in this journal, and I therefore do not recommend it for publication.
Recommendation
Reject
Author: Yili Wang on 2026-01-19 [id 6249]
(in reply to Report 1 on 2026-01-18)We thank the referee for their careful reading. While dimensional analysis provides guidance, the explicit computations are necessary to rigorously confirm the scaling of fermionic and bosonic self-energies in SYK-rised couplings. These calculations are nontrivial: they require careful treatment of multi-dimensional integrals, disorder averaging, and subtle effects such as logarithmic corrections in two dimensions, which cannot be inferred from power counting alone. Therefore, the explicit analysis is essential to validate the general conclusions.
In fact, the situation is not entirely straightforward. For example, in the presence of a Fermi sea, the naive scaling dimension of the vector differs significantly from that in the vacuum theory. Properly determining the scaling dimension requires a careful, step-by-step evaluation of the Feynman diagrams.
Moreover, if the results were truly obvious and could be obtained solely through dimensional analysis, it is unclear why such a theory, which reproduces the puzzling linear resistivity, has not been anticipated beforehand. In this sense, the referee’s comment resembles the notion of a “Columbus’ egg.” One of the contributions of this work is that we have demonstrated how these complex calculations can be approached in a relatively simple and systematic way, while simultaneously confirming the expectations through explicit computation, which is a point that appears to have been underappreciated in the report.