Monte Carlo evaluation of path integrals for the nuclear shell model.
Monte Carlo evaluation of path integrals for the nuclear shell model.
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核壳模型路径积分的蒙特卡罗评估。
DOI：
10.1103/physrevc.48.1518
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Ormand
中科院分区：
文献类型：
--
作者：
Lang;Johnson;Koonin;Ormand
我们详细介绍了壳体模型的路径积分公式和蒙特卡罗方法。用辅助场线性化二体相互作用的形式是相当普遍的，无论是在有效的“一体式”哈密顿量形式上，还是在系综的选择上。特别地，我们推导了一般(超越单极)配对算符的使用公式，以及通过活动展开来提取正则(固定粒子数)系综的新方法。我们讨论了各种公式和系综的优缺点，并给出了几个说明性的例子。我们还讨论和说明了虚时间响应函数的计算和用最大熵方法提取相应的强度函数。最后，我们讨论了费米子蒙特卡罗计算中的“符号问题”，并证明了一大类相互作用是不受这一限制的。
We present in detail a formulation of the shell model as a path integral and Monte Carlo techniques for its evaluation. The formulation, which linearizes the two-body interaction by an auxiliary field, is quite general, both in the form of the effective ‘‘one-body’’ Hamiltonian and in the choice of ensemble. In particular, we derive formulas for the use of general (beyond monopole) pairing operators, as well as a novel extraction of the canonical (fixed-particle-number) ensemble via an activity expansion. We discuss the advantages and disadvantages of the various formulations and ensembles and give several illustrative examples. We also discuss and illustrate calculation of the imaginary-time response function and the extraction, by maximum entropy methods, of the corresponding strength function. Finally, we discuss the "sign problem" generic to fermion Monte Carlo calculations, and prove that a wide class of interactions are free of this limitation.