Soliton states from quadratic electron-phonon interaction

We present a numerically exact study of self-trapped (also referred to as soliton) states of electrons that form in materials with strong quadratic coupling to the phonon coordinates. Previous studies failed to observe predictions based on the variational approach in continuum space because soliton states form only when system parameters are taken to the extreme limit. At the variational level, we establish that finite-radius solitons emerge through the weak first-order transition as the coupling strength is increased, and subsequently collapse to the single-site state through a strong first-order transition. Both transitions transform into smooth crossovers between the light and heavy polaron states in the full quantum treatment. The most surprising effect not observed in other polaron models is the nonmonotonic dependence of the soliton effective mass and the residue at strong coupling.