在辅助场蒙特卡罗方法中稳定正则包绕计算
Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
摘要：
量子蒙特卡罗方法是研究强相互作用费米系统的有力手段。然而，在具有有限精度算法的计算机上实现这些方法需要仔细注意数值稳定性。在二维场蒙特卡罗（AFMC）方法中，低温或大模型空间计算需要数值稳定的矩阵乘法。当将巨正则系综中使用的方法适应于固定粒子数的正则系综时，数值稳定化增加了计算单粒子模型空间大小的一个因子所需的浮点运算的数量，从而可以极大地限制可以研究的系统。我们描述了一种改进的方法，稳定的正则系综计算AFMC表现出更好的缩放，并提出了数值试验，证明了该方法的准确性和改进的性能。
英文摘要：
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.
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