虚时投影连续统量子Monte Carlo中的费米子符号问题
On the Fermion Sign Problem in Imaginary-Time Projection Continuum Quantum Monte Carlo with Local Interaction
摘要：
我们使用阴影波函数形式作为一个方便的模型来研究费米子符号问题影响的所有投影量子蒙特卡罗方法在连续空间。我们证明了虚时间投影算法的效率随着粒子数量和/或时间传播的增加而呈指数衰减。此外，我们推导出一个解析表达式，连接本地化的系统的大小的符号问题，说明这一预测通过一些数值结果。最后，我们讨论了费米子符号问题的计算复杂性和减轻其严重性的方法。
英文摘要：
We use the Shadow Wave Function formalism as a convenient model to study the fermion sign problem affecting all projector Quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this prediction through some numerical results. Finally, we discuss the fermion sign problem computational complexity and methods for alleviating its severity.
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