$m^\ast$ of two-dimensional electron gas: a neural canonical transformation study

TL;DR

This paper applies a neural canonical transformation method to accurately compute the quasiparticle effective mass of a two-dimensional electron gas, revealing a suppressed effective mass at low densities that differs from previous findings.

Contribution

It introduces a neural canonical transformation approach to directly calculate the effective mass of electron gas using neural networks, providing new insights into its behavior.

Findings

Effective mass is suppressed in low-density, strong-coupling regimes.

The neural approach offers a new way to study electron correlations.

Results differ from previous theoretical reports, suggesting experimental verification.

Abstract

The quasiparticle effective mass $m^\ast$ 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.