# Phonon-mediated repulsion, sharp transitions and (quasi)self-trapping in the extended Peierls-Hubbard model

## TL;DR

This paper investigates how phonon interactions in the extended Peierls-Hubbard model induce effective repulsion and complex phase transitions, affecting the mobility and pairing of particles in a quantum chain.

## Contribution

It reveals phonon-mediated interactions cause sharp phase transitions and (quasi)self-trapping in two-particle systems, highlighting their impact on quantum transport.

## Key findings

- Phonon exchange generates effective nearest-neighbor repulsion.
- Sharp transitions lead to light dimers and flattened dispersion.
- Coupling to phonons can suppress or enhance particle mobility.

## Abstract

We study two identical fermions, or two hard-core bosons, in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. We show that exchange of phonons generates effective nearest-neighbor repulsion between particles and also gives rise to interactions that move the pair as a whole. The two-polaron phase diagram exhibits two sharp transitions, leading to light dimers at strong coupling and the flattening of the dimer dispersion at some critical values of the parameters. This dimer (quasi)self-trapping occurs at coupling strengths where single polarons are mobile. This illustrates that, depending on the strength of the phonon-mediated interactions, the coupling to phonons may completely suppress or strongly enhance quantum transport of correlated particles.