$m^\ast$ of two-dimensional electron gas: a neural canonical transformation study
This work addresses a fundamental problem in condensed matter physics for researchers studying Fermi liquid theory, though it is incremental as it builds on an existing neural method.
The study tackled the elusive effective mass of the two-dimensional electron gas using a neural canonical transformation approach, revealing a more pronounced suppression of effective mass in the low-density strong-coupling region than previously reported.
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.