AI 中文总结
本研究为非厄密格点费米子引入化学势，证明特定条件下混合蒙特卡洛算法无符号问题，明确一维自由费米子符号问题的数值属性，推导精确传播子并利用AI辅助拟合完成化学势的解析延拓。
AI 中文摘要
我们为非厄密格点费米子引入了化学势，并证明对于具有简并质量和成对化学势（μ, -μ）或（iμ, iμ）的偶数味费米子，混合蒙特卡洛（Hybrid Monte Carlo）算法不存在符号问题。对于一维自由费米子，我们证明符号问题是数值层面的而非物理层面的障碍，并推导出精确传播子，该传播子在有限格点间距下远离极点处解析，但在连续极限下变为非解析。最后，我们使用AI辅助拟合来执行从虚化学势到实化学势的解析延拓。
英文摘要
We introduce a chemical potential for non-Hermitian lattice fermions and show that, for even flavors with degenerate masses and paired chemical potentials $(μ,-μ)$ or $(iμ,iμ)$, the Hybrid Monte Carlo algorithm is free of the sign problem. For one-dimensional free fermions, we demonstrate that the sign problem is a numerical rather than physical obstruction and derive the exact propagator, which is analytic at finite lattice spacing away from its poles but becomes non-analytic in the continuum limit. Finally, we use AI-assisted fitting to perform analytic continuation from imaginary to real chemical potentials.
Comments39 pages, 13 figures
