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.

翻译：我们提出了费米子神经吉布斯态（fNGS），这是一种用于模拟强相互作用费米子有限温度性质的变分框架。fNGS从参考平均场热场双重态出发，利用神经网络变换结合虚时间演化来系统性地构建强关联。应用于掺杂费米-哈伯德模型——一个捕捉强电子关联基本特征的最小晶格模型，fNGS在广泛的温度范围、相互作用强度下，即使在大掺杂情况下，对于超出精确方法可处理尺度的系统尺寸，也能精确复现热力学能量。这些结果展示了一条可扩展的路径，通过量子态的神经网络表示来研究一维以上强关联费米子系统的有限温度性质。