Phase diagram of the Holstein polaron in one dimension

TL;DR

This paper maps out the phase diagram of the 1D Holstein polaron, identifying five distinct regimes and the crossovers between them based on coupling strength and adiabaticity, providing a comprehensive unification of polaron behaviors.

Contribution

It offers a unifying framework for understanding the crossovers between different polaron regimes in the 1D Holstein model.

Findings

Identification of five distinct polaron regimes.

Mapping of crossover boundaries in parameter space.

Clarification of adiabatic and nonadiabatic contributions.

Abstract

The behavior of the 1D Holstein polaron is described, with emphasis on lattice coarsening effects, by distinguishing between adiabatic and nonadiabatic contributions to the local correlations and dispersion properties. The original and unifying systematization of the crossovers between the different polaron behaviors, usually considered in the literature, is obtained in terms of quantum to classical, weak coupling to strong coupling, adiabatic to nonadiabatic, itinerant to self-trapped polarons and large to small polarons. It is argued that the relationship between various aspects of polaron states can be specified by five regimes: the weak-coupling regime, the regime of large adiabatic polarons, the regime of small adiabatic polarons, the regime of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of small pinned polarons for which the adiabatic and nonadiabatic contributions are inextricably mixed in the polaron dispersion properties. The crossovers between these five regimes are positioned in the parameter space of the Holstein Hamiltonian.