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arXiv · 2001.11603

Legendre-spectral Dyson equation solver with super-exponential convergence

Xinyang Dong·Dominika Zgid·Emanuel Gull·Hugo U. R. Strand
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Abstract

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.

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Xinyang Dong, Dominika Zgid, Emanuel Gull, Hugo U. R. Strand. 2020-01-30. Legendre-spectral Dyson equation solver with super-exponential convergence. https://doi.org/10.1063/5.0003145

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