Bi-Polaron and N-Polaron Binding Energies

TL;DR

This paper rigorously determines the conditions under which polarons bind or do not bind, establishing the critical U=2α for the transition and proving the absence of multi-polaron binding at high U values.

Contribution

It provides a rigorous proof of the precise transition point for polaron binding and the non-existence of multi-polaron binding at large Coulomb repulsion U.

Findings

Transition from many-body collapse to thermodynamic limit at U=2α

No multi-polaron binding occurs when U is sufficiently large

Binding occurs for some U>2α, but not at high U values

Abstract

The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2\alpha, where U is the electronic Coulomb repulsion and \alpha is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. Considering the known fact that there is binding for some U>2\alpha, these conclusions are not obvious and their proof has been an open problem for some time.