Time-dependent density-functional theory for strongly correlated electrons

Kieron Burke, Diego J. Carrascal, Jaime Ferrer +1 more

M. J. P. Hodgson, J. D. Ramsden, Jacob B. J. Chapman +2 more

By propagating the many-body Schr\"odinger equation, we determine the exact time-dependent Kohn-Sham potential for a system of strongly correlated electrons which undergo field-induced tunneling. Numerous features are entirely absent from the approximations commonly used in time-dependent density-functional theory. The self-interaction correction is strong and time dependent, owing to electron localization, and prominent dynamic spatial potential steps arise from minima in the charge density, as modified by the Coulomb interaction experienced by the partially tunneled electron.

Volodymyr Turkowski, Talat Shahnaz Rahman

Swapan K. Ghosh

Michael Ruggenthaler

In order to properly describe the dynamics of a many-particle system in strong, time-dependent fields, a nonperturbative treatment of all constituents and of their correlation is needed. An ab initio solution of the time-dependent many-body Schrödinger equation is only feasible for simple systems. Hence, for many-electron systems in intense laser fields practicable methods for solving the quantum-mechanical many-body problem are required. An formally exact approach is the time-dependent density functional theory. In this work a mathematically rigorous formulation of the foundations of this theory is given. Further the non-locality in time of the exchange-correlation functionals is examined, and we formally define the notion of "quantum memory". We investigate the fundamental process of Rabi oscillations from a density-functional point of view and find the few-level approximation to be in conflict with the basis of time-dependent density functional theory. Finally, we apply the theory to calculate the electron dynamics of C60 in intense laser pulses. Although the laser light is far off-resonant with respect to the collective modes of the C60 the multi-electron dynamics strongly influences the harmonic spectra. The efficiency of this multi-particle recollision process with respect to the usual single active electron approximation of high-order harmonic generation is estimated by two analytical models.

Volodymyr Turkowski, Talat Shahnaz Rahman

In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field.