论文标题
大型费米亚系统的参数化路径积分公式
Parametrized path integral formulation for large fermion systems
论文作者
论文摘要
相同费米子之间的交换反对称性引起了众所周知的费米子标志问题，以对分区函数的正贡献和负贡献之间的大量取消形式，从而使任何直接采样此分区函数的模拟方法指数为数，难以融合。在这项工作中，我们采用了路径积分分子动力学（PIMD），并建立在最近发现的虚拟粒子模型上，以进一步研究费米昂符号问题。我们考虑了分区函数和外推的参数性路径积分公式的方法的有效性和无效条件，以规避费米子标志问题。对于我们方法的有效区域，我们的模拟表明我们可以准确地预测大型费米昂系统的能量，这超出了传统方法中直接采样的能力。特别是，我们发现并验证了高温非相互作用颗粒或在低温下强烈排斥的相互作用颗粒的简单通用关系。
The exchange antisymmetry between identical fermions gives rise to the well known fermion sign problem, in the form of large cancellation between positive and negative contribution to the partition function, making any simulation methods which directly sample this partition function exponentially difficult to converge. In this work, we employ path integral molecular dynamics (PIMD) and build upon the recently discovered fictitious particle model to investigate the fermion sign problem further. We consider the validity and invalidity condition for the method of parametrized path integral formulation of the partition function and extrapolation to circumvent the fermion sign problem. For the valid region of our method, our simulation shows that we may give accurate prediction of the energy for large fermion systems, which is much beyond the capability of the direct sampling in the traditional method. In particular, we find and verify a simple universal relation for high temperature noninteracting particles or strongly repulsive interacting particles at low temperatures.
