Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits

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.