论文标题
用路径综合基态法的费米管系统的特性
Properties of fermionic systems with the Path-integral ground state method
论文作者
论文摘要
我们使用路径综合基态方法（Pigs pigs pigs）研究了由玻色子和费米斯组成的密切相关的多体系统。为了说明Fermi-Dirac统计数据，我们将固定节点近似实施到猪中，然后将其称为FN-PIG。非常详细地，我们讨论了我们用来在坐标表示中构建全密度运算符的对密度矩阵，该方法是该方法的重要成分。我们将谐波振荡器视为概念验证，并且作为代表量子多体系统的平台，我们探索了氦原子。纯$^4 $ HE系统演示了该方法的大多数功能。互补的，对于纯$^3 $ HE，固定节点近似解决了由反对称波函数引起的无处不在的符号问题。最后，我们调查了$^3 $ He-$^4 $ He混合物，证明了该方法的稳健性。 FN-PIG的主要特征之一是它在温度下估算任何属性$ t = 0 $的能力，而没有任何其他偏见，除了FN近似外，长期模拟的偏见也被排除在外。特别是，我们计算了混合物中相等和相反的自旋对的相关函数以及$^3 $ he动能的精确值。
We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure $^4$He systems demonstrate most of the features of the method. Complementarily, for pure $^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate $^3$He-$^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T=0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the $^3$He kinetic energy in the mixture.
