Charge singlets and orbital-selective charge density wave transitions

The possibility of "orbitally selective Mott transitions" within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion $U_1$ is insulating and another orbital, to it hybridized, small $U_{-1}$, metallic, problem long-standing debate investigation. In this paper we study an analogous phenomenon, the co-existence metallic bands system orbitals different electron-phonon coupling (EPC). To end, examine two variants bilayer Holstein model: uniform "Holstein-Metal interface" where coupling, $\lambda$, zero "metallic" layer. charge density wave (CDW) order dominates at interlayer hybridization $t_3$, but decreases eventually vanishes as $t_3$ grows, providing analog singlet (spin liquid) physics. interface case, show that CDW penetrates into metal layer forms long-range intermediate ratio inter- intra-layer hopping strengths, $1.4 \lesssim t_3/t 3.4$. This consistent occurrence CDW" regime weak $\lambda_{1} \neq 0$ exhibits order, "metallic layer" $\lambda_{-1}=0$, does not.