# Fermionic neural Gibbs states

arXiv: https://arxiv.org/abs/2512.04663 · HTML: https://mlsanity.com/paper/2512.04663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 95 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions](https://mlsanity.com/paper/2401.10190/) (2024)
- [Accurate Computation of Quantum Excited States with Neural Networks](https://mlsanity.com/paper/2308.16848/) (2023)
- [Neural Wave Functions for Superfluids](https://mlsanity.com/paper/2305.06989/) (2023)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [m^ast of two-dimensional electron gas: a neural canonical transformation study](https://mlsanity.com/paper/2201.03156/) (2022)
- [Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation](https://mlsanity.com/paper/2403.07447/) (2024)
- [Are queries and keys always relevant? A case study on Transformer wave functions](https://mlsanity.com/paper/2405.18874/) (2024)
- [Solving the Hubbard model with Neural Quantum States](https://mlsanity.com/paper/2507.02644/) (2025)
- [Positive-definite parametrization of mixed quantum states with deep neural networks](https://mlsanity.com/paper/2206.13488/) (2022)
- [Diagonalization without Diagonalization: A Direct Optimization Approach for Solid-State Density Functional Theory](https://mlsanity.com/paper/2411.05033/) (2024)

## Abstract (arXiv)

We introduce fermionic neural Gibbs states (fNGS), a variational framework for modeling finite-temperature properties of strongly interacting fermions. fNGS starts from a reference mean-field thermofield-double state and uses neural-network transformations together with imaginary-time evolution to systematically build strong correlations. Applied to the doped Fermi-Hubbard model, a minimal lattice model capturing essential features of strong electronic correlations, fNGS accurately reproduces thermal energies over a broad range of temperatures, interaction strengths, even at large dopings, for system sizes beyond the reach of exact methods. These results demonstrate a scalable route to studying finite-temperature properties of strongly correlated fermionic systems beyond one dimension with neural-network representations of quantum states.