Soliton States From Quadratic Electron-Phonon Interaction

TL;DR

This paper provides a numerically exact analysis of soliton states arising from quadratic electron-phonon interactions, revealing novel transition behaviors and non-monotonic effective mass dependence.

Contribution

It is the first to numerically confirm the formation and transition of soliton states in systems with quadratic electron-phonon coupling, challenging previous variational predictions.

Findings

Finite-radius solitons emerge via weak first-order transition.

Solitons collapse to single-site states through strong first-order transition.

Non-monotonic dependence of soliton effective mass at strong coupling.

Abstract

We present the first numerically exact study of self-trapped, a.k.a. 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 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 any other polaron model is non-monotonic dependence of the soliton effective mass and the residue at strong coupling.