Self-consistent time-local approach to polaron problems
David Reichman, Columbia University
The cumulant or "linked cluster" approach has been frequently employed in condensed phase electronic structure theory as a means of correcting GW theory to describe quasi-particle spectra. The approach has roots as well in the time-local theory of master equations and is the standard approach to compute optical linehapes in the condensed phase chemical physics literature. Despite its widespread use, it has never been systematically tested, and to date has only been employed in a perturbative manner. In this talk I discuss the application of the cumulant approach to study the finite temperature spectral function of the Holstein model where comparison to exact calculations may be made. I show that the standard second order cumulant approach is only accurate for spectra near the bottom of the band unless the coupling to the bath is very small[1]. Next I discuss the formulation of a self-consistent cumulant theory[2]. This approach has some shortcomings, but appears to correct many deficits of the perturbative cumulant approach.
[1]https://arxiv.org/abs/2203.02449
[2]https://arxiv.org/abs/2203.02450