Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. I. Formalism

Abstract

Simulations of interacting electrons and bosons out of equilibrium, starting from first principles and aiming at realistic multiscale scenarios, is a grand theoretical challenge. Here, using the formalism of nonequilibrium Green's functions and relying in a crucial way on the recently discovered time-linear formulation of the Kadanoff-Baym equations, we present a versatile toolbox for the simulation of correlated electron-boson dynamics. A large class of methods are available, from the Ehrenfest to the dressed $GD$ for the treatment of electron-boson interactions in combination with perturbative, i.e., Hartree-Fock and second-Born, or nonperturbative, i.e., $GW$ and $T$-matrices either without or with exchange effects, for the treatment of the Coulomb interaction. In all cases the numerical scaling is linear in time and the equations of motion satisfy all fundamental conservation laws.

11 pages, 5 figures

References in corpus (11)

• Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5
• {\it Ab--initio} finite temperature excitons
• Real-time GW: Toward an ab initio description of the ultrafast carrier and exciton dynamics in two-dimensional materials
• Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium
• Linear optical response of current-carrying molecular junction: A NEGF-TDDFT approach
• Phonon-assisted inter-valley scattering determines ultrafast exciton dynamics in MoSe${}_2$ bilayers
• Dynamically screened vertex correction to $GW$
• Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons
• Electronic transport in molecular junctions: The generalized Kadanoff-Baym ansatz with initial contact and correlations
• Effects of photon field on heat transport through a quantum wire attached to leads
• Doublon production in correlated materials by multiple ion impacts

Cited by in corpus (25)

• A many-body approach to transport in quantum systems: From the transient regime to the stationary state
• Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
• Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons
• Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
• Non-equilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory
• Theory of coherent phonons coupled to excitons
• Nonequilibrium diagrammatic many-body simulations with quantics tensor trains
• Interacting electrons and bosons in the doubly screened $G\tilde{W}$ approximation: A time-linear scaling method for first-principles simulations
• High-harmonic spectroscopy of strongly bound excitons in solids
• Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
• Excitonic Bloch equations from first principles
• Electroluminescence rectification and high harmonic generation in molecular junctions
• Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains
• Chirped amplitude mode in photo-excited superconductors
• Ultrafast Charge Separation Induced by a Uniform Field in Graphene Nanoribbons
• Thermoelectric energy conversion in molecular junctions out of equilibrium
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains
• Electron charge dynamics and charge separation: A response theory approach
• Non-Markovian quantum kinetic simulations of uniform dense plasmas: mitigating the aliasing problem
• Stability bounds for the generalized Kadanoff-Baym ansatz in the Holstein dimer
• Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
• Excitonic effects in the photocarriers dynamics of two-dimensional materials