  We study the interplay between the electron-phonon (e-ph) and on-site
electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model
on an extended one-dimensional lattice using determinant quantum Monte Carlo.
For weak e-e and e-ph interactions, we observe a competition between an
orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave
(CDW) insulating phase, with an intermediate metallic phase located between
them. For large e-e and e-ph couplings, the OSMP and CDW phases persist, while
the metallic phase develops short-range orbital correlations and becomes
insulating when both the e-e and e-ph interactions are large but comparable.
Many of our conclusions are in line with those drawn from a prior dynamical
mean field theory study of the two-orbital Hubbard-Holstein model [Phys. Rev. B
95, 12112(R) (2017)] in infinite dimension, suggesting that the competition
between the e-ph and e-e interactions in multiorbital Hubbard-Holstein models
leads to rich physics, regardless of the dimension of the system.
