Cluster expansion for ideal Fermi systems in the `fixed-node approximation'
Cluster expansion for ideal Fermi systems in the `fixed-node approximation'
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“固定节点近似”中理想费米系统的簇扩展
DOI：
10.1088/0305-4470/34/8/312
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
V. Filinov
中科院分区：
文献类型：
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作者：
V. Filinov
在过去的十年中，“固定节点近似”，众所周知的文献中，已被广泛用于强关联费米系统的热力学性质的数值处理。直接路径积分蒙特卡罗模拟的结果表明，“固定节点近似”描述的热力学性质的强耦合费米子，而在“弱和中等”简并。为了分析高度简并费米子的“固定节点近似”与直接路径积分Monte Carlo模拟结果之间差异越来越大的原因，本文用解析方法分析了理想费米子系统的“固定节点近似”的正确性。严格证明了描述理想费米子巨配分函数对数的指数为3/2的精确费米函数不能在“固定节点近似”中重现，这意味着“固定节点近似”不能给出正确的理想费米气体极限。
Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3/2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.