Legendre-spectral Dyson equation solver with super-exponential convergence
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 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of with only a few hundred expansion coefficients.
Cite
@article{arxiv.2001.11603,
title = {Legendre-spectral Dyson equation solver with super-exponential convergence},
author = {Xinyang Dong and Dominika Zgid and Emanuel Gull and Hugo U. R. Strand},
journal= {arXiv preprint arXiv:2001.11603},
year = {2020}
}