论文标题
Legendre-Spectral Dyson方程求解器，具有超指数收敛性
Legendre-spectral Dyson equation solver with super-exponential convergence
论文作者
论文摘要
热平衡中的量子多体系统可以用假想的时间格林的功能形式形式描述。然而，通过绿色功能的存储和dyson方程溶液的精确度，可以阻碍大分子或实心AB的启动问题与完全逼真的哈密顿量的治疗。我们提出了一种传统元素算法，用于解决解决这两个问题的Dyson方程。通过在Legendre系数空间中制定算法，我们的方法继承了Green函数的Legendre系列扩展的已知范围比指数更快的融合。在此基础上，Legendre多项式卷积的快速递归方法使我们能够开发具有二次缩放的Dyson方程求解器。我们通过计算穿着二阶扰动理论中的氦二聚体He $ _2 $的分离能来介绍该算法的基准。对于此系统，Legendre Spectral算法的应用使我们能够获得$ 10^{ - 9} E_H $的能量精度，只有几百个扩展系数。
Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution, enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He$_2$ within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of $10^{-9} E_h$ with only a few hundred expansion coefficients.
