The Green's Function of the Holstein Polaron

Abstract

We present a novel, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling, and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.

21 pages, 54 figures

References in corpus (34)

• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors
• Superconductivity in Fullerides
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• The Holstein Polaron
• Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors
• Density matrix renormalization group study of the polaron problem in the Holstein model
• Polaron in t-J model
• Dynamical mean-field theory of the small polaron
• Polarons and bipolarons in strongly interacting electron-phonon systems
• Green's function of a dressed particle
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• Polaron band formation in the Holstein model
• Dimensionality effects on the Holstein polaron
• Orbital ordering phenomena in $d$- and $f$-electron systems
• On the self-trapping problem of electrons or excitons in one dimension
• Quantum Monte Carlo and variational approaches to the Holstein model
• Dynamical Properties of small Polarons
• Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model
• Single hole spectral function and spin-charge separation in the t-J model
• Spectral function of electron-phonon models by cluster perturbation theory
• Polaron effective mass from Monte Carlo simulations
• Photoemission spectra of many-polaron systems
• Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron
• A new variational approach for the Holstein Molecular Crystal Model
• Calculation of excited polaron states in the Holstein model
• Variational study of the Holstein polaron
• The Self-Trapping Line of the Holstein Molecular Crystal Model in One Dimension
• Effects of dimensionality and anisotropy on the Holstein polaron
• Polaron features of the one-dimensional Holstein Molecular Crystal Model
• Spectral Properties of Holstein and Breathing Polarons
• Photoemission spectroscopy and sum rules in dilute electron-phonon systems
• A variational approach to the optimized phonon technique for electron-phonon problems
• Holstein polaron in two and three dimensions by quantum Monte Carlo

Cited by in corpus (82)

• Froehlich Polaron and Bipolaron: Recent Developments
• Holstein polaron in a valley-degenerate two-dimensional semiconductor
• Light Bipolarons Stabilized by Peierls Electron-Phonon Coupling
• Effect of Holstein phonons on the electronic properties of graphene
• Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron
• Diagrammatic Monte Carlo method for many-polaron problems
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Band dispersion and electronic lifetimes in crystalline organic semiconductors
• Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model
• Tunable Holstein model with cold polar molecules
• Polarons and slow quantum phonons
• Charge-density-wave melting in the one-dimensional Holstein model
• Unconventional Excitonic States with Phonon Sidebands in Layered Silicon Diphosphide
• Polaron formation in the presence of Rashba spin-orbit coupling: implications for spintronics
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Electronic polarons and bipolarons in Fe-based superconductors: a pairing mechanism
• Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
• Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Towards Outperforming Classical Algorithms with Analog Quantum Simulators
• The polaron paradigm: a dual coupling effective band model
• Trapping of three-dimensional Holstein polarons by various impurities
• Single polaron properties of the breathing-mode Hamiltonian
• Bond-Peierls polaron: Moderate mass enhancement and current-carrying ground state
• Coexistence of excited polarons and metastable delocalized states in photo-induced metals
• Holstein polaron in the presence of disorder
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Going beyond the linear approximation in describing electron- phonon coupling: relevance for the Holstein model
• Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer
• Phase diagram of the Holstein polaron in one dimension
• Single polaron properties for double-well electron-phonon coupling
• Discontinuous polaron transition in a two-band model
• Peierls versus Holstein models for describing electron-phonon coupling in perovskites
• Emergence of states in the phonon spectral function of the Holstein polaron below and above the one-phonon continuum
• Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems
• Survival of the Dirac points in rippled graphene
• Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons
• The effects of non-linear electron-phonon interactions on superconductivity and charge-density-wave correlations
• Ferromagnetic spin-polaron on complex lattices
• Holstein polaron: the effect of multiple phonon modes
• Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations
• Strongly bound yet light bipolarons for double-well electron-phonon coupling
• Polaronic approach to strongly correlated electron system with strong electron-phonon interaction
• Cumulant expansion in the Holstein model: Spectral functions and mobility
• Quantum simulation of extended polaron models using compound atom-ion systems
• Surface Polaron Formation in the Holstein model
• Green's function variational approach to orbital polarons in KCuF3
• Diagrammatic content of the DMFT for the Holstein polaron problem in finite dimensions
• Phonon-assisted carrier motion on the Wannier-Stark ladder
• Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
• Holstein polarons, Rashba-like spin splitting and Ising superconductivity in electron-doped MoSe2
• Neutral triplet Collective Mode as a new decay channel in Graphite
• Exciton dissociation mediated by phonons in organic photovoltaics
• Inhomogeneous dynamical mean field theory of the small polaron problem
• The end points in the dispersion of Holstein polarons
• A perturbational study of the lifetime of a Holstein polaron in the presence of weak disorder
• Orbital Effects of Strong Magnetic Field on a 2-D Holstein Polaron
• Short-range antiferromagnetic correlation effect on conduction electrons in two-dimensional strongly correlated electron systems
• The Generalized Green's function Cluster Expansion: A Python package for simulating polarons
• Light bipolarons in a system of electrons coupled to dispersive optical phonons
• Exact solution of electronic transport in semiconductors dominated by scattering on polaronic impurities
• Generalized Dynamical Keldysh Model
• Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning
• Periodically driven small polarons
• Spectral Function of an Electron Coupled to Hard Core Bosons
• Electron addition spectral functions of low-density polaron liquids
• Physically interpretable approximations of many-body spectral functions
• Holstein magneto-polarons: from Landau levels to Hofstadter butterflies
• Spectral function of a bipolaron coupled to dispersive optical phonons
• Dichotomy of electron-phonon interactions in the delafossite PdCoO${}_2$: From weak bulk to polaronic surface coupling
• Generalization of correlated electron-ion dynamics from nonequilibrium Green's functions
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Spectral signatures of residual electron pairing in the extended-Hubbard-Su-Schrieffer-Heeger model
• Adiabatic theory of the polaron spectral function
• Bound excited states of Fröhlich polarons in one dimension
• Extending the Feynman variational principle and analytical methods to lattice polarons
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems
• Going Beyond the Cumulant Approximation: Power Series Correction to Single Particle Green's Function in Holstein System
• Cumulant methods for electron-phonon problems. I. Perturbative expansions
• Self-consistent approach to the dynamics of excitation energy transfer in multichromophoric systems
• Band-selective Holstein polaron in Luttinger liquid material A0.3MoO3 (A = K, Rb)