Numerical study of the electron-phonon interaction in multiorbital materials

This thesis examines the electron-phonon (e-ph) interaction in multiorbital correlated systems using various numerical techniques, including determinant quantum Monte Carlo and dynamical mean field theory. First, I studied the non-linear e-ph coupling in a one band model and found that even a weak non-linear e-ph couplings can significantly shape both electronic and phononic properties. Second, I study the interplay between the e-ph and electron-electron (e-e) interactions in a multiorbital Hubbard-Holstein model in both one- and infinite-dimension. In both cases, I found that a weak e-ph interaction is enough to induce a phase transition from the Mott phase to the charge-density-wave phase. Moreover, I find that not only the e-e correlation but also the e-ph interaction can induce an orbital-selective phase. Our results imply that the e-ph interaction is significant in the multiorbital correlated materials, such as the iron-based superconductors. Last, I studied the offdiagonal e-ph interaction in a two-dimensional three-orbital model defined on a Lieb lattice. I consider an sp-type model, which is like a 2D analog of the barium bismuthate high temperature superconductors. I found a metal-to-insulator (MI) transition as decreasing temperature at half filling and identified a dimerized structure in the insulating phase. With hole doping, the ordered polarons and bipolarons correlations disappear but the short-range correlations are present, implying that polarons and bipolarons preform in the matellic phase and freeze into a periodic array in the insulating state. In sum, this thesis reveals the importance of the e-ph interaction in the multiorbital materials and gives an alarm to people when study these multiorbital materials.