# Soliton States From Quadratic Electron-Phonon Interaction

**Authors:** Zhongjin Zhang, Anatoly Kuklov, Nikolay Prokof'ev, Boris Svistunov  
**arXiv:** [2309.10669](https://arxiv.org/abs/2309.10669)  
**Date:** 2023-09-19  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.10669v1/

## Key points

- First numerically exact investigation of self-trapped states of electrons
- Soliton states form in materials with strong quadratic coupling to phonon coordinates
- Previous studies failed to observe predictions based on variational approach in continuum space
- Finite-radius solitons arise through weak first-order transition as coupling strength increases
- Solitons undergo smooth crossover between light and heavy polaron states instead of collapsing into single-site state
- Non-monotonic dependence of soliton effective mass and residue at strong coupling observed, not seen in other polaron models
- Provides valuable insights into soliton states formed by electrons with strong quadratic coupling to phonon coordinates
- Numerical analysis offers precise understanding of self-trapped electron states
- Highlights phenomena such as weak and strong first-order transitions and non-monotonic behavior at high coupling strengths

## Summary

In their study, Zhongjin Zhang, Anatoly Kuklov, Nikolay Prokof'ev, and Boris Svistunov present the first numerically exact investigation of self-trapped states of electrons, also known as soliton states, that form in materials with strong quadratic coupling to the phonon coordinates. Previous studies have failed to observe predictions based on the variational approach in continuum space because soliton states only emerge when system parameters are taken to the extreme limit. At the variational level, the authors establish that finite-radius solitons arise through a weak first-order transition as the coupling strength is increased. These solitons subsequently undergo a smooth crossover between light and heavy polaron states rather than collapsing into a single-site state through a strong first-order transition as previously thought. The most surprising finding in this study is the non-monotonic dependence of the soliton effective mass and residue at strong coupling. This effect has not been observed in any other polaron model. Overall, this research provides valuable insights into soliton states formed by electrons with strong quadratic coupling to phonon coordinates. The authors' numerical analysis offers a precise understanding of these self-trapped electron states and highlights important phenomena such as weak and strong first-order transitions and non-monotonic behavior at high coupling strengths.