论文标题
使用Bogoliubov的不平等和热力学整合，在路径积分蒙特卡洛模拟中减轻费米的标志问题
Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
论文作者
论文摘要
使用路径积分蒙特卡洛（PIMC）方法对相关的费物进行的准确热力学模拟对于许多应用，例如对超电原子的描述，量子点中的电子和温暖的物质至关重要。主要障碍是费米亚标志问题（FSP），它导致计算时间的指数增加，随着系统大小的增加和温度降低。最近，Hirshberg等人。 [J。化学物理。 152，171102（2020）]提议根据Bogoliubov不平等来减轻FSP。在目前的工作中，我们通过添加一个控制扰动的参数来扩展此方法，从而允许外推到确切的结果。通过这种方式，我们还可以使用热力学整合来获得改进的费米子能量估计。作为测试系统，我们选择2D和3D量子点中的电子，在某些情况下，与标准PIMC相比，在某些情况下发现了超过10^6的速度，同时保持相对精度为$ \ sim0.1 \％$。我们的方法非常通用，可以很容易地适应其他仿真方法。
Accurate thermodynamic simulations of correlated fermions using path integral Monte Carlo (PIMC) methods are of paramount importance for many applications such as the description of ultracold atoms, electrons in quantum dots, and warm-dense matter. The main obstacle is the fermion sign problem (FSP), which leads to an exponential increase in computation time both with increasing the system-size and with decreasing temperature. Very recently, Hirshberg et al. [J. Chem. Phys. 152, 171102 (2020)] have proposed to alleviate the FSP based on the Bogoliubov inequality. In the present work, we extend this approach by adding a parameter that controls the perturbation, allowing for an extrapolation to the exact result. In this way, we can also use thermodynamic integration to obtain an improved estimate of the fermionic energy. As a test system, we choose electrons in 2D and 3D quantum dots and find in some cases a speed-up exceeding 10^6 , as compared to standard PIMC, while retaining a relative accuracy of $\sim0.1\%$. Our approach is quite general and can readily be adapted to other simulation methods.
