Achieving the Ultimate Scaling Limit for Nonequilibrium Green Functions Simulations

Abstract

The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is nonequilibrium Green functions (NEGF). However, NEGF simulations are computationally expensive due to their $T^3$ scaling with the simulation duration $T$. Recently, $T^2$ scaling was achieved with the generalized Kadanoff--Baym ansatz (GKBA) which has substantially extended the scope of NEGF simulations. Here we present a novel approach to GKBA-NEGF simulations that is of order $T$, and demonstrate its remarkable capabilities.

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Cited by in corpus (54)

• Ab initio simulation of warm dense matter
• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• Ultrafast dynamics of electrons and phonons: from the two-temperature model to the time-dependent Boltzmann equation
• Fast Green's function method for ultrafast electron-boson dynamics
• The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
• Real-time GW: Toward an ab initio description of the ultrafast carrier and exciton dynamics in two-dimensional materials
• Low rank compression in the numerical solution of the nonequilibrium Dyson equation
• Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium
• Restricted configuration path integral Monte Carlo
• Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. I. Formalism
• The dynamically screened ladder approximation: Simultaneous treatment of strong electronic correlations and dynamical screening out of equilibrium
• 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
• Photoinduced dynamics of organic molecules using nonequilibrium Green's functions with second-Born, $GW$, $T$-matrix and three-particle ladder correlations
• Shock Physics in Warm Dense Matter--a quantum hydrodynamics perspective
• Adaptive Numerical Solution of Kadanoff-Baym Equations
• Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons
• Photo-induced nonequilibrium states in Mott insulators
• A quantum Boltzmann equation for strongly correlated electrons
• A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes
• Memory truncated Kadanoff-Baym equations
• Revealing Ultrafast Phonon Mediated Inter-Valley Scattering through Transient Absorption and High Harmonic Spectroscopies
• Non-equilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory
• 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
• Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
• Adaptive Time Stepping for the Two-Time Integro-Differential Kadanoff-Baym Equations
• Quantum fluctuations approach to the nonequilibrium $GW$ approximation
• Ionization potential depression and Fermi barrier in warm dense matter--a first--principles approach
• Electron correlation effects in superconducting nanowires in and out of equilibrium
• Accelerating Nonequilibrium Green functions simulations with embedding selfenergies
• Neutralization dynamics of slow highly charged ions passing through graphene nanoflakes--an embedding self-energy approach
• Excitonic Bloch equations from first principles
• Estimates of the dynamic structure factor for the finite temperature electron liquid via analytic continuation of path integral Monte Carlo data
• Doublon production in correlated materials by multiple ion impacts
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• Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains
• Classical and Quantum Theory of Fluctuations for Many-Particle Systems out of Equilibrium
• Electroluminescence rectification and high harmonic generation in molecular junctions
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Quantum Fluctuations Approach to the Nonequilibrium $GW$-Approximation II: Density Correlations and Dynamic Structure Factor
• Coherence and de-coherence in the Time-Resolved ARPES of realistic materials: an ab-initio perspective
• Two-Time Quantum Fluctuations Approach and its Relation to the Bethe--Salpeter Equation
• Ultrafast Charge Separation Induced by a Uniform Field in Graphene Nanoribbons
• Interacting electrons in a flat-band system within the Generalized Kadanoff-Baym Ansatz
• Thermoelectric energy conversion in molecular junctions out of equilibrium
• A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains
• Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures
• Few-Photon Fluorescence from Ultracold Bosons in an Optical Cavity
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
• Non-Markovian quantum kinetic simulations of uniform dense plasmas: mitigating the aliasing problem
• Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
• Stability bounds for the generalized Kadanoff-Baym ansatz in the Holstein dimer