We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $M$th-order diagram at inverse temperature $\beta$ from $\mathcal{O}(\beta^{2M-1})$ for a direct quadrature to $\mathcal{O}(M \log^{M+1} \beta)$, with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multi-band impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca$_2$RuO$_4$, demonstrating the promise of the method for modeling realistic strongly correlated multi-band materials. For expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust black-box evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams.

翻译：我们提出一种确定性算法，用于高效评估基于最近引入的虚时格林函数离散莱曼表示（DLR）的虚时费曼图。除利用其近似性质实现图解积分的高效离散化外，DLR基在虚时上具有可分离性，使得我们能够将费曼图分解为嵌套序列的一维乘积与卷积的线性组合。以广义安德森杂质模型的强耦合粗线展开为核心，我们证明该策略将逆温度β下M阶费曼图的计算复杂度从直接求积法的𝒪(β^{2M-1})降至𝒪(M log^{M+1} β)，同时具备可控的高阶精度。我们通过对含非对角杂化与自旋-轨道耦合的多带杂质问题进行三阶展开的基准测试，并与严格对角化及量子蒙特卡洛方法进行对比。特别地，我们针对描述Ca₂RuO₄最小模型的三带哈伯德模型开展自洽动力学平均场理论计算，其中包含强自旋-轨道耦合，展示了该方法在模拟真实强关联多带材料中的潜力。对于可枚举费曼图的低阶及中阶展开，本方法提供了一种高效、直接且稳健的黑箱评估流程。由此，它填补了低阶图解近似（虽简单廉价但精度不足）与基于蒙特卡洛高阶图采样方法之间的空白。