论文标题
关于费米昂模型中的无限差异问题
On the Infinite Variance Problem in Fermion Models
论文作者
论文摘要
蒙特卡洛计算具有连续辅助场的费米子系统经常遭受不同的差异。如果系统存在无限差异问题，那么即使使用无限数量的样本，也无法可靠地估计可观察到的物品。在本文中，我们探讨了一种基于采样的方法，该方法是根据带有额外时间板的系统的分布来处理的。必要的重新加权因子是扰动和通过次要蒙特卡洛计算的。我们表明，蒙特卡洛重新净化与使用无偏见的重新净化因子的估计量相结合的方法导致一种方法，该方法以很小的额外成本消除了无限差异问题。我们在半填充时计算哈伯德模型中的双重占用率，以证明该方法并将结果与通过其他方法获得的完善结果进行比较。
Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number of samples. In this paper, we explore a method to deal with this problem based on sampling according to the distribution of a system with an extra time-slice. The necessary reweighting factor is computed both perturbatively and through a secondary Monte Carlo. We show that the Monte Carlo reweigthing coupled to the use of a non-biased estimator of the reweigthing factor leads to a method that eliminates the infinite variance problem at a very small extra cost. We compute the double occupancy in the Hubbard model at half-filling to demonstrate the method and compare the results to well established results obtained by other methods.
