Vertex corrections to conductivity in the Holstein model: A numerical-analytical study

Abstract

The optical-conductivity profile carries information on electronic dynamics in interacting quantum many-body systems. Its computation is a formidable task that is usually approached by invoking the single-particle (bubble) approximation and neglecting the vertex corrections, the importance of which remains elusive even in model Hamiltonian calculations. Here, we combine analytical arguments with our recent breakthroughs in numerically exact and approximate calculations of finite-temperature real-time correlation functions to thoroughly assess the importance of vertex corrections in the one-dimensional Holstein polaron model. We find, both analytically and numerically, vanishing vertex corrections to optical conductivity in the limits of zero electron--phonon interaction, zero electronic bandwidth, and infinite temperature. Furthermore, our numerical results show that vertex corrections to the electron mobility also vanish in many parameter regimes between these limits. In some of these cases, the vertex corrections still introduce important qualitative changes to the optical-conductivity profile in comparison to the bubble approximation even though the self-energy remains approximately local. We trace these changes back to the bubble approximation not fully capturing a time-limited slow-down of the electron on intermediate time scales between ballistic and diffusive transport. We find that the vertex corrections are overall most pronounced for intermediate electron--phonon interaction and may increase or decrease the bubble-approximation mobility depending on the values of model parameters.

Final, published version; main text: 28 pages, 12 figures; supplementary material: 13 pages, 5 figures

References in corpus (27)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• Band-like motion and mobility saturation in organic molecular semiconductors
• Dynamical mean-field theory of the small polaron
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Green's function of a dressed particle
• Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections
• Mobility of Holstein polaron: an unbiased approach
• Dynamical properties of the one-dimensional Holstein model
• 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${}_3$
• Analytical continuation of imaginary axis data for optical conductivity
• Spectral weight function for the half-filled Hubbard model: a singular value decomposition approach
• A unification of the Holstein polaron and dynamic disorder pictures of charge transport in organic semiconductors
• Optical properties of small polarons from dynamical mean-field theory
• On dynamical localization corrections to band transport
• Crossover from Super- to Sub-Diffusive Motion and Memory Effects in Crystalline Organic Semiconductors
• Calculation of excited polaron states in the Holstein model
• Optical conductivity of the Holstein polaron
• Intermediate Polaronic Charge Transport in Organic Crystals from a Many-Body First-Principles Approach
• Optical absorption and activated transport in polaronic systems
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations
• Cumulant expansion in the Holstein model: Spectral functions and mobility
• Anomalous transport of small polarons arises from transient lattice relaxation or immovable boundaries
• Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors

Cited by in corpus (9)

• Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-Classical Solutions
• Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime
• Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Conductivity of lattice bosons at high temperatures
• Identification of the transport regimes of the one-dimensional Holstein model
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Quantum-classical study of charge transport in organic semiconductors with multiple low-frequency vibrational modes
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems