Going Beyond the Cumulant Approximation II:Power Series Correction to Single Particle Green's Function in 1D Holstein Chain

TL;DR

This paper introduces an ODE-based power series correction method for the single particle Green's function in 1D Holstein chains, improving accuracy over the cumulant approximation and matching exact results across various coupling strengths.

Contribution

It develops a scalable, inexpensive differential formalism for power series correction that surpasses the cumulant approximation in modeling 1D Holstein chains.

Findings

Excellent agreement with exact diagonalization results.

Effective modeling of carrier mass growth and energy displacement.

Heuristic prediction of satellite structures.

Abstract

Previously, we introduced a method for systematically correcting a quasiparticle green's function via a power series expansion. Here we present an ODE based formalisms of power series correction that goes beyond the cumulant approximation and implement it to 1D Holstein chain for a wide range of coupling strengths in a scalable and inexpensive fashion at both zero and finite temperature. We show that this first differential formalism of the power series is both qualitatively and quantitatively in excellent agreement with exact diagonalization results on 1D Holstein chain with dispersive bosons for a large range of electron-boson coupling strength. We investigate carrier mass growth rate and carrier energy displacement across a wide range of coupling strength. Finally, we present a heuristic argument which predicts most of the rich satellite structure without explicit calculation.