Cumulant methods for electron-phonon problems. I. Perturbative expansions

Abstract

In this work we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CE for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for non-zero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant, and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials.

arXiv comment16 pages, 7 figures

References in corpus (26)

• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Electron-phonon interactions from first principles
• Froehlich Polaron and Bipolaron: Recent Developments
• Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals
• The Holstein Polaron
• Origin of the crossover from polarons to Fermi liquids in transition metal oxides
• Ab initio theory of polarons: formalism and applications
• Green's function of a dressed particle
• Polarons from first principles, without supercells
• The Green's Function of the Holstein Polaron
• Dimensionality effects on the Holstein polaron
• Dynamical Properties of small Polarons
• Spectral Functions of the Uniform Electron Gas via Coupled-Cluster Theory and Comparison to the $GW$ and Related Approximations
• Light Bipolarons Stabilized by Peierls Electron-Phonon Coupling
• Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron
• Mobility of Holstein polaron: an unbiased approach
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO${}_3$
• Spectral properties of the 2D Holstein polaron
• Spectral function of electron-phonon models by cluster perturbation theory
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Polaron mobility in the "beyond quasiparticles" regime
• Intermediate Polaronic Charge Transport in Organic Crystals from a Many-Body First-Principles Approach
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems
• Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion