Discontinuous polaron transition in a two-band model

We present exact diagonalization and momentum average approximation (MA) results for the single polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=\pi$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-band nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multi-band models in higher dimensions.