论文标题
实时绿色功能的激发和光谱
Excitations and spectra from equilibrium real-time Green's functions
论文作者
论文摘要
Green功能的实时轮廓形式主义提供了量子多体系统的时间相关信息。实际上，由于离散的Green功能的存储要求和求解Dyson方程的计算成本，对具有广泛能量尺度的系统的长期模拟都具有挑战性。在本手稿中，我们基于一部分高阶正交多物质扩展来实时离散化，以解决这些问题。我们提出了一种用于使用Legendre光谱法和用于Legendre卷积的递归算法来求解实时平衡dyson方程的超融合算法。我们表明，紧凑的高阶离散化与我们的dyson求解器结合使用，可以使用比常规多步法方法所需的离散点要少得多的仿真。作为概念的证明，我们使用自consistent的二阶扰动理论来计算h $ _2 $，lih，lih，lih，lih，lih，lih，he $ _2 $和c $ _6 $ _4 $ _4 $ _4 $ _4 $ _4 $ _4 $ _4 $ _4 $ _4 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _6 $ _2 $的分子光谱函数的分子光谱函数，并将结果与标准量子化学方法均无均等。
The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this manuscript, we apply a real-time discretization based on a piece-wise high-order orthogonal-polynomial expansion to address these issues. We present a superconvergent algorithm for solving the real-time equilibrium Dyson equation using the Legendre spectral method and the recursive algorithm for Legendre convolution. We show that the compact high order discretization in combination with our Dyson solver enables long-time simulations using far fewer discretization points than needed in conventional multistep methods. As a proof of concept, we compute the molecular spectral functions of H$_2$, LiH, He$_2$ and C$_6$H$_4$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.
