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 $\beta$ and spectral width $\omega_{\max}$ from $\mathcal{O}((\beta \omega_{\max})^{2M-1})$ for a direct quadrature to $\mathcal{O}(M (\log (\beta \omega_{\max}))^{M+1})$, 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 both strong and weak coupling 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：我们提出了一种基于近期引入的虚时格林函数离散莱曼表示（DLR）的确定性算法，用于高效评估虚时图。DLR基不仅通过其逼近性质实现了图解积分的有效离散化，还具有虚时可分离性，从而允许我们将图分解为多个一维乘积与卷积嵌套序列的线性组合。针对广义安德森杂质模型的强耦合粗线展开，我们证明该策略可将评估逆温度β和谱宽ω_max下的M阶图的计算复杂度从直接积分的𝒪((β ω_max)^(2M-1))降低至𝒪(M (log (β ω_max))^(M+1))，同时实现可控的高阶精度。我们利用三阶展开对具有非对角杂化与自旋-轨道耦合的多带杂质问题进行基准测试，并与精确对角化及量子蒙特卡洛方法进行比较。特别地，我们对代表Ca₂RuO₄最小模型的三带哈伯德模型进行了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相关多带材料方面的潜力。对于低阶和中阶的强耦合与弱耦合展开（其中图可枚举），我们的方法提供了一种高效、直接且鲁棒的黑箱评估过程。从这一意义上看，它填补了简单廉价但不精确的最低阶图近似与基于高阶图蒙特卡洛采样的方法之间的空白。