用神经网络构建强关联费米子的热态，突破传统方法规模限制。
Fermionic neural Gibbs states
- 基于平均场热双态，结合神经网络与虚时演化构建关联
- 在大掺杂、宽温域下精准复现哈伯德模型热能
- 适用于超越一维的强关联费米系统，可扩展至精确方法无法处理的尺寸
我们提出费米子神经吉布斯态（fNGS），一种用于建模强相互作用费米子有限温度性质的变分框架。fNGS从参考平均场热双态出发，利用神经网络变换与虚时演化系统地引入强关联。应用于掺杂费米-哈伯德模型（一种捕捉强电子关联本质特征的最小晶格模型），fNGS在广泛温度范围、相互作用强度及大掺杂情况下，均能准确复现热能，且适用于精确方法难以处理的系统尺寸。结果表明，该方法为借助神经网络量子态表示，在一维以外体系中研究强关联费米系统的有限温度性质提供了可扩展路径。
原文摘要 · Abstract (English)
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.
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