Achieving the 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), for second order Born (SOA) selfenergies, which has substantially extended the scope of NEGF simulations. Here we demonstrate that GKBA-NEGF simulations can be performed with order T 1 scaling, both for SOA and GW selfenergies, and point out the remarkable capabilities of this approach.

Ab initio simulation of warm dense matter

“…Theoretical methods for WDM out of equilibrium are even more challenging than equilibrium applications that were discussed above. They include time-dependent DFT [69,219], semiclassical kinetics [78], quantum kinetic theory and nonequilibrium Green functions [44,83,220,221], hydrodynamics [80,88,222] or rate equations [223]. Among the problems that were studied are the equilibration of the electron distribution by electron-electron collisions [83,220], non-thermal melting induced by fs xray pulses [219], the density response for nonequilibrium momentum distributions [79,221], density evolution following short-pulse laser excitation [78], collisional heating of quantum plasmas by a laser pulse [224,225], or ionization dynamics in a short laser pulse [80].…”

“…During the last 25 years, improved and generalized quantum kinetic equations have been derived starting from reduced density operators, e.g. [39,40], or nonequilibrium Green functions (NEGF) [41][42][43][44], for text books see [40,[45][46][47] and references therein. Another direction in quantum plasma theory is first principle computer simulations such as quantum Monte Carlo [4,[48][49][50][51][52][53][54][55], semiclassical molecular dynamics with quantum potentials (SC-MD), e.g.…”

Discrete memory kernel for multitime correlations in non-Markovian quantum processes

“…These projection operators are analogous to the standard Nakajima-Zwanzig projectors [6]; notice, however, that they are defined directly on the dynamical tensor and not on the underlying SE dynamics. 3 Making use of the identity, we can iteratively decompose the dynamical tensor as…”

“…Modeling the dynamical properties of open quantum systems is an outstanding challenge in modern physics. Applications range from studying impurity dynamics in ultracold quantum gases or strongly correlated materials [1][2][3], to modeling emission properties of organic molecules or artificial atoms [4,5]. While a plethora of techniques exists for the simulation of the time dependence of observables at a single point in time [6,7], usually encoded in the time-dependent state of an open system, there are relatively few that are aimed at computing multitime correlation functions in full generality.…”

Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium

“…While this approach was acknowledged and used already in the 1990s [34][35][36][37][38], its recent revival [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] has made it possible to combine the NEGF approach with ab initio descriptions of realistic atomic, molecular, and condensed matter systems [57][58][59][60][61]. Recent development has further allowed for an equivalent but more efficient representation of the GKBA time evolution with only a linear scaling in the number of time steps [62][63][64].…”