Differential Formalism of Power Series Correction for Single particle Electron Green's Function: Applications to 1D Holstein Chain.*

Based on our previous work on self-consistent power series correction formalism¹ present for single particle green's function we present two ODE based formalisms of Power series correction that go beyond the cumulant approximation and are scalable and fast. The first differential formalism of the power series gives the exact results on the Holstein chain for a large range or electron-boson coupling constant and is faster than the self-consistent formalism. The second differential formalism is even faster but faces severe instability for the same problem when the boson energy scale is comparable or smaller than the band width. We discuss this instability and show that it stems from the assumption made on the nature of correction to simplify the correction form. We finally discuss its implication to self-consistent cumulant expansion.

[1] B. Pandey and P.B. Littlewood, Phys. Rev. Lett. 129, 136401