The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this paper, we apply a real-time discretization based on a piecewise high-order orthogonal-polynomial expansion to address these issues. We present a superconvergent algorithm for solving the real-time equilibrium Dyson equation using the Legendre spectral method and the recursive algorithm for Legendre convolution. We show that the compact high-order discretization in combination with our Dyson solver enables long-time simulations using far fewer discretization points than needed in conventional multistep methods. As a proof of concept, we compute the molecular spectral functions of ${\mathrm{H}}_2$, LiH, ${\mathrm{He}}_2$, and ${\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{O}}_2$ using self-consistent second-order perturbation theory and compare the results with standard quantum chemistry methods as well as the auxiliary second-order Green's function perturbation theory method.

中文翻译：

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来自平衡实时格林函数的激发和光谱

格林函数的实时轮廓形式提供了量子多体系统的时间相关信息。在实践中，由于离散格林函数的存储要求和求解戴森方程的计算成本，对具有广泛能量尺度的系统进行长期模拟具有挑战性。在本文中，我们应用基于分段高阶正交多项式展开的实时离散化来解决这些问题。我们提出了一种使用勒让德谱法和勒让德卷积的递归算法求解实时平衡戴森方程的超收敛算法。我们表明，紧凑的高阶离散化与我们的 Dyson 求解器相结合，可以使用比传统多步方法所需的离散化点少得多的长时间模拟。作为概念证明，我们计算了分子光谱函数${\mathrm{H}}_2$, 锂,${他}_2$， 和${\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{○}}_2$使用自洽二阶微扰理论并将结果与​​标准量子化学方法以及辅助二阶格林函数微扰理论方法进行比较。