Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion

Abstract

In this work we present a self-consistent cumulant expansion (SC-CE) and investigate its accuracy for the one-dimensional Holstein model with and without phonon dispersion. We show that for finite lattices sizes, the numerical integration of the SC-CE equations becomes unstable at long times. This defect is partially ameliorated when studying systems in the thermodynamic limit, enabling the demonstration that the SC-CE corrects many deficits of the standard perturbative CE in the (non-dispersive) Holstein model. The natural phonon damping that arises in the more realistic dispersed Holstein model renders the SC-CE stable, allowing for a complete assessment of the method. Here we find that self-consistency dramatically corrects many of the failures found in the perturbative CE, but also introduces some unphysical features. Finally, we comment on the potential use of SC-CE as a tool for calculating Green's functions in generic many-body problems.

11 pages, 4 figures

References in corpus (2)

• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene

Cited by in corpus (4)

• Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons
• Cumulant expansion in the Holstein model: Spectral functions and mobility
• Cumulant methods for electron-phonon problems. I. Perturbative expansions
• Going Beyond the Cumulant Approximation: Power Series Correction to Single Particle Green's Function in Holstein System