Excitations and spectra from equilibrium real-time Green's functions

TL;DR

This paper introduces a high-order orthogonal-polynomial discretization method for real-time Green's functions, enabling efficient long-time simulations of quantum many-body systems with reduced computational resources.

Contribution

The authors develop a superconvergent Legendre spectral algorithm for solving the equilibrium Dyson equation, improving long-time simulation efficiency in quantum many-body physics.

Findings

Enables long-time Green's function simulations with fewer discretization points.

Accurately computes molecular spectral functions for various molecules.

Demonstrates compatibility with self-consistent second-order perturbation theory.

Abstract

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.