Date of Award


Degree Type


Degree Name

Doctor of Philosophy



Major Professor

Steven S. Johnston

Committee Members

Elbio R. Dagotto, Takeshi Egami, Thomas A. Maier, Hanno Weitering


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.


Portions of this document were previously published in the following journal Europhysics Letters 109, 27002 (2015) Phys. Rev. B 92, 064301 (2015) Phys. Rev. E 93, 063313 (2016) Phys. Rev, B 94, 235126 (2016) Phys. Rev. B 95, 121112(R) (2017)

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