Competing phases and orbital-selective behaviors in the two-orbital Hubbard-Holstein model

In recent years, electron-electron (e-e) interactions in multiorbital Hubbard models have been widely studied. However, surprisingly little is known about how multiorbital phenomena like the orbital-selective Mott phase (OSMP) are affected by the electron-phonon (e-ph) interaction. In this talk, we present a study of the interplay between e-e and e-ph interactions in the degenerate two-orbital Hubbard-Holstein model at half filling using the dynamical mean-field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the underlying phase diagram of this model, reshaping the orbital-selective behavior and introducing a new orbital-selective phase, the orbital-selective Peierls phase (OSPI). Specifically, at small e-e and e-ph couplings, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between the Mott and charge-density-wave (CDW) phases. We further demonstrate that the Hund’s coupling favors the OSPI transition by lowering the energy associated with the CDW. Our results are important since many researchers have dismissed the relevance of the e-ph interaction in the iron-based superconductors due to an early predictions of weak e-ph interaction strengths. [Phys. Rev. B 95, 121112(R) (2017)]