Quantum fluctuations approach to the nonequilibrium $GW$ approximation

Abstract

The quantum dynamics of fermionic or bosonic many-body systems following external excitation can be successfully studied using two-time nonequilibrium Green's functions (NEGF) or single-time reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle self-energy or decoupling of the BBGKY hierarchy. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. Here, we develop a different approach where, instead of equations of motion for the many-particle NEGF (or density operators), single-time equations for the correlation functions of fluctuations are analyzed. We present a derivation of the first two equations of the alternative hierarchy of fluctuations and discuss possible decoupling approximations. In particular, we derive the polarization approximation (PA) which is shown to be equivalent to the single-time version [following by applying the generalized Kadanoff-Baym ansatz (GKBA)] of the nonequilibrium $GW$ approximation with exchange effects of NEGF theory, for weak coupling. The main advantage of the quantum fluctuations approach is that the standard ensemble average can be replaced by a semiclassical average over different initial realizations, as was demonstrated before by Lacroix and co-workers [see e.g. D. Lacroix et al., Phys. Rev. B, 2014, 90, 125112]. Here, we introduce the stochastic $GW$ (SGW) approximation and the stochastic polarization approximation (SPA) which are demonstrated to be equivalent to the single-time $GW$ approximation without and with exchange, respectively, in the weak coupling limit. Our numerical tests confirm that our approach has the same favorable linear scaling with the computation time as the recently developed G1-G2 scheme [Schluenzen et al., Phys. Rev. Lett., 2020, 124, 076601].

arXiv comment36 pages, 14 figures

References in corpus (17)

• A Stochastic Mean-Field Approach For Nuclear Dynamics
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations
• Achieving the Ultimate Scaling Limit for Nonequilibrium Green Functions Simulations
• Nonequilibrium dynamics in the one-dimensional Fermi-Hubbard model: A comparison of the nonequilibrium Green functions approach and the density matrix renormalization group method
• Hubbard nanoclusters far from equilibrium
• The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
• Ab initio transport results for strongly correlated fermions
• Simulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories
• Ultrafast dynamics of finite Hubbard clusters - a stochastic mean-field approach
• The dynamically screened ladder approximation: Simultaneous treatment of strong electronic correlations and dynamical screening out of equilibrium
• Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study
• Time Evolution of Non-Equilibrium Effective Action
• Analysis of continuous and discrete Wigner approximations for spin dynamics
• Impact of the initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study
• Importance of realistic phase space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions
• Reliable spin-transfer torque driven precessional magnetization reversal with an adiabatically decaying pulse

Cited by in corpus (8)

• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
• Accelerating Nonequilibrium Green functions simulations with embedding selfenergies
• Classical and Quantum Theory of Fluctuations for Many-Particle Systems out of Equilibrium
• Quantum Fluctuations Approach to the Nonequilibrium $GW$-Approximation II: Density Correlations and Dynamic Structure Factor
• Two-Time Quantum Fluctuations Approach and its Relation to the Bethe--Salpeter Equation
• On the Klimontovich description of complex (dusty) plasmas