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

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