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m* of two-dimensional electron gas: A neural canonical transformation study

by Hao Xie, Linfeng Zhang, and Lei Wang

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Hao Xie
Submission information
Preprint Link: scipost_202210_00081v2  (pdf)
Code repository:
Date accepted: 2023-04-11
Date submitted: 2023-02-10 16:47
Submitted by: Xie, Hao
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approach: Computational


The quasiparticle effective mass m* of interacting electrons is a fundamental quantity in the Fermi liquid theory. However, the precise value of the effective mass of uniform electron gas is still elusive after decades of research. The newly developed neural canonical transformation approach [Xie et al., J. Mach. Learn. 1, (2022)] offers a principled way to extract the effective mass of electron gas by directly calculating the thermal entropy at low temperature. The approach models a variational many-electron density matrix using two generative neural networks: an autoregressive model for momentum occupation and a normalizing flow for electron coordinates. Our calculation reveals a suppression of effective mass in the two-dimensional spin-polarized electron gas, which is more pronounced than previous reports in the low-density strong-coupling region. This prediction calls for verification in two-dimensional electron gas experiments.

List of changes

1. Update Fig. 4 to include data for rs = 0.5 and 0.25.
2. Report relevant benchmark values in the caption of Fig. 2 and S1.
3. Clarify the error analysis of effective mass from the original data; add data processing scripts to the public code repository for reproduction of the final results.
4. Make slight modifications to some phrases and sentences.

Published as SciPost Phys. 14, 154 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-3-18 (Invited Report)


I am satisfied with authors' response to the critical remarks and with the revisions made.

I recommend publishing the manuscript .

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

Anonymous Report 1 on 2023-3-8 (Invited Report)


(see my previous report)


(see my previous report)


I am in general satisfied with the revisions and the replies made by the authors, as well as the updates to the open source repo.
As I wrote before, it is a challenging problem and the application of ML to it is certainly in the high risk category, but I fully endorse such non-trivial studies.
I am nevertheless still surprised by the non-monotonicity of the data with N in the low rs regime. The authors mention that a finite size analysis of the interacting model does not exist, but I recall from various Monte Carlo approaches that the extrapolation to the thermodynamic limit is usually under a (surprisingly) good control despite the low particle numbers involved. I will give the authors the benefit of the doubt.

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

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