SciPost Submission Page
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
|Authors (as registered SciPost users):||Hao Xie|
|Preprint Link:||scipost_202210_00081v2 (pdf)|
|Date submitted:||2023-02-10 16:47|
|Submitted by:||Xie, Hao|
|Submitted to:||SciPost Physics|
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.
Published as SciPost Phys. 14, 154 (2023)
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.
Submission & Refereeing History
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Reports on this Submission
(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.