The breakdown of adiabatic polaron theory in one, two, and three   dimensions and the reformation of the large polaron concept
  We prove variationally that at weak coupling in one, two, and three dimensions there exist correlated electron-phonon states below the approximate ground states characteristically found by adiabatic polaron theory. Besides differing non-trivially in quantitative aspects such as the value of the ground state energy, these improved ground states are found to differ significantly in qualitative aspects such as correlation structure and scaling behavior. These differences are sufficiently severe as to require a reevaluation of the physical meaning attached to such widely used terms as "large polaron" and "self-trapping transition". 
Aldo H. Romero, David W. Brown and Katja Lindenberg