Interacting Holstein and extended-Holstein bipolarons

TL;DR

This study investigates bipolaron interactions in Holstein-Hubbard and extended-Holstein-Hubbard models, revealing no attraction in the former and clear attraction leading to composite bipolarons in the latter, with phase diagrams illustrating these phenomena.

Contribution

It introduces a self-consistent variational basis generation scheme and applies DMRG to analyze bipolaron interactions, highlighting the formation of composite bipolarons in the extended-Holstein-Hubbard model.

Findings

No bipolaron-bipolaron attraction in Holstein-Hubbard model.

Bipolaron-bipolaron attraction in F2H model leading to composite bipolarons.

Phase diagram of F2H polarons and bipolarons, with phase separation analysis.

Abstract

Employing the recently developed self-consistent variational basis generation scheme, we have investigated the bipolaron-bipolaron interaction within the purview of Holstein-Hubbard and the extended-Holstein-Hubbard (F2H) model on a discrete one-dimensional lattice. The density-matrix renormalization group (DMRG) method has also been used for the Holstein-Hubbard model. We have shown that there exists no bipolaron-bipolaron attraction in the Holstein-Hubbard model. In contrast, we have obtained clear-cut bipolaron-bipolaron attraction in the F2H model. Composite bipolarons are formed above a critical electron-phonon coupling strength, which can survive the finite Hubbard $U$ effect. We have constructed the phase diagram of F2H polarons and bipolarons, and discussed the phase separation in terms of the formation of composite bipolarons.