Fermionic neural Gibbs states

TL;DR

This paper presents fermionic neural Gibbs states (fNGS), a neural network-based variational method for accurately modeling finite-temperature properties of strongly interacting fermions, including complex systems like the doped Fermi-Hubbard model.

Contribution

It introduces a novel neural-network framework combining mean-field states and imaginary-time evolution to efficiently capture correlations in fermionic systems at finite temperature.

Findings

Accurately reproduces thermal energies across various temperatures and interactions.

Effective for large system sizes beyond exact methods.

Demonstrates scalability for studying complex fermionic systems.

Abstract

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.