全组态相互作用量子蒙特卡罗中的布居控制偏差和重要抽样
Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
摘要：
人口控制是任何投影蒙特卡罗算法的重要组成部分。这种控制机制通常会在抽样数量中引入与总体规模成反比的偏差。本文研究了全组态相互作用量子蒙特卡罗方法中的布居控制偏置。我们确定了这种偏见的确切来源，并在一般情况下对其进行量化。我们表明，它有不同的影响，不同的估计和移位估计是特别敏感。我们推导出一个重新加权的技术，类似于在扩散蒙特卡罗中使用的，用于纠正这种偏见，并将其应用到移位估计。我们还表明，通过使用重要性抽样，偏差可以大大减少。我们证明了应用这些技术的必要性和有效性的无符号问题的系统，这种偏见是特别显着的。具体来说，我们显示的结果为大的一维哈伯德模型和二维海森堡模型，其中校正FCIQMC结果与其他高精度的结果。
英文摘要：
Population control is an essential component of any projector Monte Carlo algorithm. This control mechanism usually introduces a bias in the sampled quantities that is inversely proportional to the population size. In this paper, we investigate the population control bias in the full configuration interaction quantum Monte Carlo method. We identify the precise origin of this bias and quantify it in general. We show that it has different effects on different estimators and that the shift estimator is particularly susceptible. We derive a re-weighting technique, similar to the one used in diffusion Monte Carlo, for correcting this bias and apply it to the shift estimator. We also show that by using importance sampling, the bias can be reduced substantially. We demonstrate the necessity and the effectiveness of applying these techniques for sign-problem-free systems where this bias is especially notable. Specifically, we show results for large one-dimensional Hubbard models and the two-dimensional Heisenberg model, where corrected FCIQMC results are comparable to the other high-accuracy results.
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