Cumulant expansion in the Holstein model: Spectral functions and mobility

Abstract

We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory (DMFT) which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law $\mu \propto T^{-2}$ in the limit of weak coupling and $\mu \propto T^{-3/2}$ for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.

arXiv comment22 pages, 14 figures + supp.mat. 12 pages, 9 figures

References in corpus (26)

• Electron-phonon interactions from first principles
• The transient localization scenario for charge transport in crystalline organic materials
• Tunable polaronic conduction in anatase TiO2
• Density matrix renormalization group study of the polaron problem in the Holstein model
• Dynamical mean-field theory of the small polaron
• Origin of the crossover from polarons to Fermi liquids in transition metal oxides
• Green's function of a dressed particle
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• The Green's Function of the Holstein Polaron
• Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron
• Dynamical properties of the one-dimensional Holstein model
• Diagrammatic Monte Carlo method for many-polaron problems
• Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO${}_3$
• Optical properties of small polarons from dynamical mean-field theory
• On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Cumulant expansion for phonon contributions to the electron spectral function
• Intermediate Polaronic Charge Transport in Organic Crystals from a Many-Body First-Principles Approach
• Cumulant Green's function calculations of plasmon satellites in bulk sodium: influence of screening and the crystal environment
• Spectral Fingerprints of Electron-Plasmon Coupling
• Satellite structures in the spectral functions of semiconductor quantum well two-dimensional electron gases: a GW plus cumulant study
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Photoemission spectroscopy and sum rules in dilute electron-phonon systems
• Dispersion and lineshape of plasmon satellites in one, two and three dimensions
• Accuracy of approximate methods for the calculation of absorption-type linear spectra with a complex system-bath coupling
• Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion

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• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Nonperturbative self-consistent electron-phonon spectral functions and transport
• Identification of the transport regimes of the one-dimensional Holstein model
• Mixed Quantum-Classical Methods for Polaron Spectral Functions
• Signature of preformed pairs in angle-resolved photoemission spectroscopy
• Spectral function of a bipolaron coupled to dispersive optical phonons
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems