Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics

Abstract

The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using time-resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Currently, however, real-time Green's function simulations are either prohibitively expensive due to the cubic scaling with the propagation time or do neglect the feedback of electrons on the bosons, thus violating energy conservation. We put forward a computationally efficient Green's function scheme which overcomes both limitations. The numerical effort scales linearly with the propagation time while the simultaneous dressing of electrons and bosons guarantees the fulfillment of all fundamental conservation laws. We present a real-time study of the phonon-driven relaxation dynamics in an optically excited narrow band-gap insulator, highlighting the nonthermal behavior of the phononic degrees of freedom. Our formulation paves the way to first-principles simulations of electron-boson systems with unprecedented long propagation times.

Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons

“…The two contributions are equal in the absence of -interactions as has been shown in our earlier work [34]. Notice that , c contains a phononic part (equal to ph c ) and a purecorrelation energy.…”

“…We are close to achieving the goal of ps dynamics within a NEGF theory: -ph thermalization has already been demon-strated in a model insulator without -interactions on a 2 ps time-scale [34], whereas -interacting 2D systems have been propagated for 100 fs [35]. Here, we illustrate our methods by applying them to electron-phonon ( -ph) dynamics in the 1D Holstein-Hubbard model [30,36].…”

“…In paper I we have shown using the generalized Kadanoff-Baym ansatz (GKBA) [39] that they, in turn, fulfill their own equations of motions: for electrons in 2B and approximations [40,41]  ( ) = −Ψ ( ) + ( ) + ρ Δ ( ) ( )  ( ) −  ( ) ( ) + ( )ρ Δ ( ) . (10) And, similarly, for phonons [34]  ph ( ) = −Ψ ph ( ) + ph ( ) ph ( ) −  ph ( ) ( ), (11) We consistently use bold symbols to denote rank-2 matrices with phononic indices (viz. Eq.…”

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

“…The electron dynamics in correlated materials is typically accompanied by the interaction with bosonic particles and quasiparticles, such as phonons, plasmons, charge density waves, photons, etc.. From the theoretical point of view the vastly different energy (or time) scales [1][2][3][4][5][6] and the quantum nature of the involved bosonic particles [7][8][9][10][11] pose considerable challenges. A scalable quantum method to model excitation and relaxation phenomena in correlated many-body systems, reliable beyond the perturbative regime, is crucial to simulate and interpret experimental results and to design new materials.…”

“…In our recent Letter [11] we extended the GKBA to quantized bosonic particles and formulated a first-order ODE, hence timelinear, scheme to treat systems with an electron-boson ( -) interaction. We also stated that it is possible to include the electron-electron ( -) interactions on equal footing.…”