Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

Physical Review B 134308 (2018)

Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

Shunsuke A. Sato, Aaron Kelly, Angel Rubio

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled for- ward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems.

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We acknowledge financial support from the European Research Council(ERC-2015-AdG-694097), Grupos Consolidados (IT578-13), European Union's H2020 programme under GA no.676580 (NOMAD) and Alexander von Humboldt Foundation. AK acknowledges funding from the National Sciences and Engineering Research Council of Canada (NSERC) Discovery grant program,and start-up funding from Dalhousie University.

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