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

TL;DR

This paper investigates how increasing electron-phonon coupling in the Holstein model affects polaron and bipolaron formation, revealing that bipolaronic metal-insulator transitions depend on the electron spin state and coupling regime, using DMFT and analytical methods.

Contribution

It provides a comparative analysis of polaron and bipolaron formation in the Holstein model across different regimes, combining numerical DMFT results with analytical approaches.

Findings

Bipolaronic binding causes a metal-insulator transition in the spinful case.

Polaron formation does not necessarily lead to a metal-insulator transition.

The Born-Oppenheimer approximation breaks down at the polaron crossover.

Abstract

The evolution of the properties of a finite density electronic system as the electron-phonon coupling is increased are investigated in the Holstein model using the Dynamical Mean-Field Theory (DMFT). We compare the spinless fermion case, in which only isolated polarons can be formed, with the spinful model in which the polarons can bind and form bipolarons. In the latter case, the bipolaronic binding occurs through a metal-insulator transition. In the adiabatic regime in which the phonon energy is small with respect to the electron hopping we compare numerically exact DMFT results with an analytical scheme inspired by the Born-Oppenheimer procedure. Within the latter approach,a truncation of the phononic Hilbert space leads to a mapping of the original model onto an Anderson spin-fermion model. In the anti-adiabatic regime (where the phonon energy exceeds the electronic scales) the standard treatment based on Lang-Firsov canonical transformation allows to map the original model on to an attractive Hubbard model in the spinful case. The separate analysis of the two regimes supports the numerical evidence that polaron formation is not necessarily associated to a metal-insulator transition, which is instead due to pairing between the carriers. At the polaron crossover the Born-Oppenheimer approximation is shown to break down due to the entanglement of the electron-phonon state.