用归一化流方法解决掺杂哈伯德模型的符号问题，提升模拟精度与效率。
Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows
- 引入退火方案，实现自洽采样，克服自旋基下的遍历性瓶颈。
- 相比主流电荷基混合蒙特卡洛，统计误差降低一个数量级。
- 适合研究掺杂关联电子系统，为强关联系统模拟提供新路径。
在有限化学势下的哈伯德模型是理解掺杂关联体系的核心，但受制于符号问题，数值模拟面临巨大挑战。在辅助场表述中，自旋基可缓解符号问题，但严重的遍历性问题限制了其应用。本文将近期在半填满时基于归一化流的进展扩展至有限化学势，引入退火方案实现遍历采样。相较于最先进的电荷基混合蒙特卡洛方法，该方法能准确复现精确对角化结果，同时将统计不确定性降低一个数量级，为掺杂关联系统的模拟开辟新途径。
原文摘要 · Abstract (English)
The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.
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