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

arXiv: https://arxiv.org/abs/2201.03156 · HTML: https://mlsanity.com/paper/2201.03156/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 103 references that are in the map.
- First posted on arXiv 10 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Learning Differential Equations that are Easy to Solve](https://mlsanity.com/paper/2007.04504/) (2020)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Neural Density Estimation and Likelihood-free Inference](https://mlsanity.com/paper/1910.13233/) (2019)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Neural Networks with Cheap Differential Operators](https://mlsanity.com/paper/1912.03579/) (2019)
- [Ab-initio study of interacting fermions at finite temperature with neural canonical transformation](https://mlsanity.com/paper/2105.08644/) (2021)
- [Inferring the quantum density matrix with machine learning](https://mlsanity.com/paper/1904.05903/) (2019)

## Built on by (most cited first, 7 of 7)

- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Deep Variational Free Energy Approach to Dense Hydrogen](https://mlsanity.com/paper/2209.06095/) (2022)
- [Deep generative modelling of canonical ensemble with differentiable thermal properties](https://mlsanity.com/paper/2404.18404/) (2024)
- [A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation](https://mlsanity.com/paper/2406.00047/) (2024)
- [Accurate and thermodynamically consistent hydrogen equation of state for planetary modeling with flow matching](https://mlsanity.com/paper/2501.10594/) (2025)
- [Fermionic neural Gibbs states](https://mlsanity.com/paper/2512.04663/) (2025)
- [Quantum Dynamics via Score Matching on Bohmian Trajectories](https://mlsanity.com/paper/2604.25137/) (2026)

## Abstract (arXiv)

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.