Electronic frictional effects near metal surfaces with strong correlations

The electronic friction-Langevin dynamics (EF-LD) offers a simplified framework for describing nonadiabatic effects at metal surfaces, particularly in electrochemical and molecular electronic applications. We investigate the electronic friction behavior for the Hubbard–Holstein model using density matrix renormalization group (DMRG) theory. We show that electron–electron interactions lead to the formation of two energy levels in the impurity, resulting in two peaks in the electronic friction at the resonances of electron attachment or detachment with the metal’s Fermi level. We further benchmark our results against mean field theory (MFT) and exact diagonalization (ED). The results calculated by ED and DMRG show strong agreement at high temperatures, suggesting that the results from DMRG are reliable; however, at low temperatures, ED exhibits significant deviations relative to DMRG due to the finite-size limitations inherent in ED calculations. MFT completely fails to recover the Fermi resonance in electronic friction. Moreover, we investigate the dynamics of the electronic friction using EF-LD. Simulations reveal differences between the electronic population and kinetic energy dynamics predicted by MFT and DMRG approaches, suggesting that the MFT approach is unreliable for nonadiabatic dynamics of strongly correlated systems.