Legendre-spectral Dyson equation solver with super-exponential convergence.

Area of Science:

• Quantum many-body physics
• Computational chemistry
• Materials science

Background:

• Quantum systems in equilibrium use imaginary time Green's function formalism.
• Large-scale ab initio calculations face challenges in Green's function storage and Dyson equation precision.

Purpose of the Study:

• To present a novel Legendre-spectral algorithm for solving the Dyson equation.
• To address storage and precision limitations in quantum many-body calculations.

Main Methods:

• Formulating the Dyson equation in Legendre coefficient space.
• Utilizing fast recursive methods for Legendre polynomial convolution.
• Developing a Dyson equation solver with quadratic scaling.

Main Results:

• Achieved faster-than-exponential convergence due to Legendre series expansion.
• Demonstrated quadratic scaling for the Dyson equation solver.
• Computed the dissociation energy of He2 with 10^-9 Eh accuracy.

Conclusions:

• The Legendre-spectral algorithm offers an efficient and accurate solution for quantum many-body problems.
• This method significantly enhances the treatment of large molecular and solid systems.
• The algorithm provides high precision with a reduced number of expansion coefficients.