Going Beyond the Cumulant Approximation: Power Series Correction to Single Particle Green's Function in Holstein System

TL;DR

This paper introduces a power series correction method for single particle Green's functions in a Holstein system, improving upon cumulant approximations by matching exact spectral functions across different regimes.

Contribution

It develops a general PSC scheme to correct Green's functions and compares it with cumulant and exact methods, revealing regimes where cumulant fails and PSC succeeds.

Findings

PSC spectral functions match exact results within spectral broadening

Identifies regimes where cumulant approximation fails

Provides a systematic correction scheme for Green's functions

Abstract

In the context of a single electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct single particle Green's function using a power series correction(PSC) scheme. We then outline the derivations of various flavors of cumulant approximation through the PSC scheme and explain the assumptions and approximations behind them. Finally, we compute and compare PSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem - two that cumulant explains and one where cumulant fails. We find that the exact and the PSC spectral functions match within spectral broadening across all three regimes.