论文标题
量子杂质模型的假颗粒顶点求解器
Pseudoparticle vertex solver for quantum impurity models
论文作者
论文摘要
我们根据伪粒子框架提出了一个量子杂质求解器，该框架结合了三点顶点的示意图与四点顶点的图表蒙特卡洛采样。这种最近提出的方法[A。 J. Kim等人，Arxiv：2112.15549]在此处概括为费米子杂质问题，我们讨论了实施的技术细节，包括时间步长的方法，蒙特卡洛更新以及检查四点顶点的两粒子不可及的例程。我们还解释了如何使用Dubiner基础表示如何有效地存储顶点信息。该算法的收敛属性通过应用于单一轨道哈伯德模型的准确溶解杂质模型和动力学均值仿真模拟。此外，该算法可以处理异性杂交杂交的两轨问题，这将在标准杂交 - 扩张 - 蒙特卡洛模拟中引起严重的符号问题。由于基于顶点的算法成功地处理了平衡中的符号振荡积分，仅样品仅连接的图表，这可能是实时模拟的一种有希望的方法。
We present a quantum impurity solver based on a pseudo-particle 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.
