Polaron Crossover and Bipolaronic Metal-Insulator Transition in the half- filled Holstein model

TL;DR

This paper investigates the transition from polaronic to bipolaronic states in the Holstein model, revealing that bipolaron formation drives the metal-insulator transition, using Dynamical Mean-Field Theory and various approximation methods.

Contribution

It distinguishes polaron crossover from bipolaron formation and compares exact DMFT solutions with perturbative and vertex correction approaches.

Findings

Polaron formation does not cause a metal-insulator transition.

Bipolaron formation is responsible for the transition.

Exact DMFT results differ from perturbative approximations.

Abstract

The formation of a finite density multipolaronic state is analyzed in the context of the Holstein model using the Dynamical Mean-Field Theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of Dynamical Mean-Field Theory is compared with weak-coupling perturbation theory, non-crossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated to a metal-insulator transition, which is instead due to bipolaron formation.