开放量子系统的尺蠖蒙特卡罗方法
Inchworm Monte Carlo method for open quantum systems
摘要：
本文研究了最近提出的一种用于开放量子系统的图形量子蒙特卡罗方法--尺蠖蒙特卡罗方法。在Dyson级数的重新证明的基础上，我们严格地证明了它的有效性。此外，我们引入了一个积分微分方程制定的开放量子系统，这说明了尺蠖算法的数学结构。这种新的配方导致改进的尺蠖算法，通过引入经典的确定性时间积分计划。数值方法的验证应用到自旋玻色子模型。
英文摘要：
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover, we introduce an integro-differential equation formulation for open quantum systems, which illuminates the mathematical structure of the inchworm algorithm. This new formulation leads to an improvement of the inchworm algorithm by introducing classical deterministic time-integration schemes. The numerical method is validated by applications to the spin-boson model.
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