克服均匀系统中的费米子符号问题
Overcoming the fermion sign problem in homogeneous systems
摘要：
在路径积分蒙特卡罗（PIMC）中显式处理多体费米统计导致指数缩放的计算成本，这是由于偶数和奇数排列对观测量的贡献几乎抵消。通过对交换统计的直接分析，我们发现，除了有限尺寸效应外，均匀系统中的个体交换概率与其他排列的构型无关。对于两个有代表性的系统，3-He和均匀的电子气，我们表明，这使得整个反对称化的密度矩阵从一个简单的模型产生依赖于只有几个参数直接从一个标准的PIMC模拟。其结果是一个多项式的缩放算法和高达10个数量级的增加，在测量费米子可观的系统考虑的效率。
英文摘要：
Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through direct analysis of exchange statistics we find that individual exchange probabilities in homogeneous systems are, except for finite size effects, independent of the configuration of other permutations present. For two representative systems, 3-He and the homogeneous electron gas, we show that this allows the entire antisymmetrized density matrix to be generated from a simple model depending on only a few parameters obtainable directly from a standard PIMC simulation. The result is a polynomial scaling algorithm and up to a 10 order of magnitude increase in efficiency in measuring fermionic observables for the systems considered.
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