We present a quantum impurity solver based on a pseudoparticle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach (A. J. Kim et al., arXiv:2112.15549) is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign-oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.

中文翻译：

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量子杂质模型的伪粒子顶点求解器

我们提出了一种基于赝粒子框架的量子杂质求解器，它将三点顶点的图解恢复与四点顶点的图解蒙特卡罗采样相结合。这种最近提出的方法（AJ Kim等人。, arXiv:2112.15549）在这里被推广到费米子杂质问题，我们讨论了实现的技术细节，包括时间步长方法、蒙特卡罗更新以及检查四点顶点的两粒子不可约性的例程. 我们还解释了如何使用 Dubiner 基表示有效地存储顶点信息。该算法的收敛特性通过应用于精确可解的杂质模型和单轨道哈伯德模型的动态平均场理论模拟得到证明。进一步表明，该算法可以处理非对角线杂交的双轨道问题，这将在标准杂交-扩展蒙特卡罗模拟中导致严重的符号问题。