Diagrammatic Monte Carlo method for many-polaron problems

Abstract

We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from renormalized Fermi-liquid to single polarons, across the non-adiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections the accuracy of theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the system density.

Published version, comparison with DMFT and Momentum Average method are added in comparison with first version

References in corpus (23)

• Polaron Problem by Diagrammatic Quantum Monte Carlo
• The Holstein Polaron
• Feynman diagrams versus Fermi-gas Feynman emulator
• Efficient DMFT-simulation of the Holstein-Hubbard Model
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• 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
• Two-dimensional Hubbard-Holstein bipolaron
• Polaron Crossover and Bipolaronic Metal-Insulator Transition in the half- filled Holstein model
• Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Holstein model in infinite dimensions at half-filling
• Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling
• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Bold Diagrammatic Monte Carlo technique for frustrated spin systems
• Optical conductivity of the Holstein polaron
• Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
• Holstein polaron in the presence of disorder
• Spin, charge and single-particle spectral functions of the one-dimensional quarter filled Holstein model
• Dynamic charge correlations near the Peierls transition
• Enumeration of many-body skeleton diagrams
• Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

Cited by in corpus (39)

• Tailoring the nature and strength of electron-phonon interactions in the SrTiO${}_3$(001) two-dimensional electron liquid
• Polaronic metal state at the LaAlO3/SrTiO3 interface
• Holstein polaron in a valley-degenerate two-dimensional semiconductor
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
• Diagrammatic Monte Carlo study of the Fröhlich polaron dispersion in 2D and 3D
• The polaron paradigm: a dual coupling effective band model
• Peierls/Su-Schrieffer-Heeger polarons in two dimensions
• Coulomb and electron-phonon interactions in metals
• High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Properties of the non-linear Holstein polaron at finite doping and temperature
• Electron-polaron dichotomy of charge carriers in perovskite oxides
• Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems
• Polaron with Quadratic Electron-phonon Interaction
• Polaron transformations in the realistic model of the strongly correlated electron system
• Cumulant expansion in the Holstein model: Spectral functions and mobility
• Machine learning for phase ordering dynamics of charge density waves
• Quantum Phase Transition of Many Interacting Spins Coupled to a Bosonic Bath: static and dynamical properties
• Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron
• Fermi blockade of the electron-phonon interaction: why strong coupling effects may not be seen in optimally doped high temperature superconductors
• Ground state features and spectral properties of large polaron liquids from low to high charge densities
• Light polarons with electron-phonon coupling
• Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states
• Polarons with arbitrary nonlinear electron-phonon interaction
• Entanglement of electrons and the lattice in a Luttinger system
• Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning
• Electron addition spectral functions of low-density polaron liquids
• Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature
• Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at $T=0$ K
• GW space-time method: Energy band-gap of solid hydrogen
• Metal-insulator transition of spinless fermions coupled to dispersive optical bosons
• Fingerprints of preformed pairs in two-electron angle-resolved photoemission spectroscopy
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions